diff --git a/.github/dependabot.yml b/.github/dependabot.yml
index e98ee6e..0232f93 100644
--- a/.github/dependabot.yml
+++ b/.github/dependabot.yml
@@ -9,14 +9,3 @@ updates:
       prefix: "ci"
       prefix-development: "ci"
       include: "scope"
-  - package-ecosystem: pip
-    directory: /
-    schedule:
-      interval: monthly
-    commit-message:
-      prefix: "build"
-      prefix-development: "build"
-      include: "scope"
-    versioning-strategy: lockfile-only
-    allow:
-      - dependency-type: "all"
diff --git a/.github/workflows/publish.yml b/.github/workflows/publish.yml
index 9acb673..fb01aa5 100644
--- a/.github/workflows/publish.yml
+++ b/.github/workflows/publish.yml
@@ -14,7 +14,7 @@ jobs:
         uses: actions/checkout@v4
 
       - name: Set up Python
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: "3.10"
 
diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 9c6c631..de285e1 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -14,7 +14,7 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        python-version: ["3.10"]
+        python-version: ["3.10", "3.11"]
 
     name: Python ${{ matrix.python-version }}
 
@@ -36,12 +36,12 @@ jobs:
           PYTHON_VERSION=${{ matrix.python-version }} devcontainer up --workspace-folder .
 
       - name: Lint package
-        run: devcontainer exec --workspace-folder . poe lint
+        run: devcontainer exec --remote-env CI=true --workspace-folder . poe lint
 
       - name: Test package
-        run: devcontainer exec --workspace-folder . poe test
+        run: devcontainer exec --remote-env CI=true --workspace-folder . poe test
 
       - name: Upload coverage
-        uses: codecov/codecov-action@v3
+        uses: codecov/codecov-action@v4
         with:
           files: reports/coverage.xml
diff --git a/README.md b/README.md
index 8f67a82..52a77c7 100644
--- a/README.md
+++ b/README.md
@@ -2,11 +2,124 @@
 
 # 👖 Conformal Tights
 
-A scikit-learn [meta-estimator](https://scikit-learn.org/stable/glossary.html#term-meta-estimator) for computing tight [conformal predictions](https://en.wikipedia.org/wiki/Conformal_prediction).
+A [scikit-learn meta-estimator](https://scikit-learn.org/stable/glossary.html#term-meta-estimator) that adds [conformal prediction](https://en.wikipedia.org/wiki/Conformal_prediction) of coherent [quantiles](https://en.wikipedia.org/wiki/Quantile) and [intervals](https://en.wikipedia.org/wiki/Prediction_interval) to any [scikit-learn regressor](https://scikit-learn.org/stable/glossary.html#term-regressor). Features:
+
+1. 🍬 *Meta-estimator*: add prediction of quantiles and intervals to any scikit-learn regressor
+2. 🌡️ *Conformally calibrated:* accurate quantiles, and intervals with reliable [coverage](https://en.wikipedia.org/wiki/Coverage_probability)
+3. 🚦 *Coherent quantiles:* quantiles increase monotonically instead of [crossing](https://github.com/dmlc/xgboost/issues/9848) [each other](https://github.com/microsoft/LightGBM/issues/3447)
+4. 👖 *Tight quantiles:* selects the lowest [dispersion](https://en.wikipedia.org/wiki/Statistical_dispersion) that provides the desired coverage
+5. 🎁 *Data efficient:* requires only a small number of calibration examples to fit
+6. 🐼 *Pandas support:* optionally predict on DataFrames and receive DataFrame output
 
 ## Using
 
-To add and install this package as a dependency of your project, run `poetry add conformal-tights`.
+### Installing
+
+First, install this package with:
+
+```sh
+pip install conformal-tights
+```
+
+### Predicting quantiles
+
+Conformal Tights exposes a meta-estimator called `ConformalCoherentQuantileRegressor` that you can use to wrap any scikit-learn regressor, after which you can use `predict_quantiles` predict conformally calibrated quantiles. Example usage:
+
+```python
+from conformal_tights import ConformalCoherentQuantileRegressor
+from sklearn.datasets import fetch_openml
+from sklearn.model_selection import train_test_split
+from xgboost import XGBRegressor
+
+# Fetch dataset and split in train and test
+X, y = fetch_openml("ames_housing", version=1, return_X_y=True, as_frame=True, parser="auto")
+X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.15, random_state=42)
+
+# Create a regressor, wrap it, and fit on the train set
+my_regressor = XGBRegressor(objective="reg:absoluteerror")
+conformal_predictor = ConformalCoherentQuantileRegressor(estimator=my_regressor)
+conformal_predictor.fit(X_train, y_train)
+
+# Predict with the wrapped regressor
+ŷ_test = conformal_predictor.predict(X_test)
+
+# Predict quantiles with the conformal wrapper
+ŷ_test_quantiles = conformal_predictor.predict_quantiles(X_test, quantiles=(0.025, 0.05, 0.1, 0.9, 0.95, 0.975))
+```
+
+When the input data is a pandas DataFrame, the output is also a pandas DataFrame. For example, printing the head of `ŷ_test_quantiles` yields:
+
+|   house_id |   0.025 |   0.05 |    0.1 |    0.9 |   0.95 |   0.975 |
+|-----------:|--------:|-------:|-------:|-------:|-------:|--------:|
+|       1357 |  121557 | 130272 | 139913 | 189399 | 211177 |  237309 |
+|       2367 |   86005 |  92617 |  98591 | 130236 | 145686 |  164766 |
+|       2822 |  116523 | 121711 | 134993 | 175583 | 194964 |  216891 |
+|       2126 |  105712 | 113784 | 122145 | 164330 | 183352 |  206224 |
+|       1544 |   85920 |  92311 |  99130 | 133228 | 148895 |  167969 |
+
+Let's visualize the predicted quantiles on the test set:
+
+<img src="https://github.com/radix-ai/conformal-tights/assets/4543654/b02b3797-de6a-4e0d-b457-ed8e50e3f42c" width="512">
+
+<details>
+<summary>Expand to see the code that generated the graph above</summary>
+
+```python
+import matplotlib.pyplot as plt
+import matplotlib.ticker as ticker
+%config InlineBackend.figure_format = "retina"
+plt.rcParams["font.size"] = 8
+idx = (-ŷ_test.sample(50, random_state=42)).sort_values().index
+y_ticks = list(range(1, len(idx) + 1))
+plt.figure(figsize=(4, 5))
+for j in range(3):
+    end = ŷ_test_quantiles.shape[1] - 1 - j
+    coverage = round(100 * (ŷ_test_quantiles.columns[end] - ŷ_test_quantiles.columns[j]))
+    plt.barh(
+        y_ticks,
+        ŷ_test_quantiles.loc[idx].iloc[:, end] - ŷ_test_quantiles.loc[idx].iloc[:, j],
+        left=ŷ_test_quantiles.loc[idx].iloc[:, j],
+        label=f"{coverage}% Prediction interval",
+        color=["#b3d9ff", "#86bfff", "#4da6ff"][j],
+    )
+plt.plot(y_test.loc[idx], y_ticks, "s", markersize=3, markerfacecolor="none", markeredgecolor="#e74c3c", label="Actual value")
+plt.plot(ŷ_test.loc[idx], y_ticks, "s", color="blue", markersize=0.6, label="Predicted value")
+plt.xlabel("House price")
+plt.ylabel("Test house index")
+plt.yticks(y_ticks, y_ticks)
+plt.tick_params(axis="y", labelsize=6)
+plt.grid(axis="x", color="lightsteelblue", linestyle=":", linewidth=0.5)
+plt.gca().xaxis.set_major_formatter(ticker.StrMethodFormatter("${x:,.0f}"))
+plt.gca().spines["top"].set_visible(False)
+plt.gca().spines["right"].set_visible(False)
+plt.legend()
+plt.tight_layout()
+plt.show()
+```
+</details>
+
+### Predicting intervals
+
+In addition to quantile prediction, you can use `predict_interval` to predict conformally calibrated prediction intervals. Compared to quantiles, these focus on reliable coverage over quantile accuracy. Example usage:
+
+```python
+# Predict an interval for each example with the conformal wrapper
+ŷ_test_interval = conformal_predictor.predict_interval(X_test, coverage=0.95)
+
+# Measure the coverage of the prediction intervals on the test set
+coverage = ((ŷ_test_interval.iloc[:, 0] <= y_test) & (y_test <= ŷ_test_interval.iloc[:, 1])).mean()
+print(coverage)  # 96.6%
+```
+
+When the input data is a pandas DataFrame, the output is also a pandas DataFrame. For example, printing the head of `ŷ_test_interval` yields:
+
+|   house_id |   0.025 |   0.975 |
+|-----------:|--------:|--------:|
+|       1357 |  108489 |  238396 |
+|       2367 |   76043 |  165189 |
+|       2822 |  101319 |  220247 |
+|       2126 |   94238 |  207501 |
+|       1544 |   75976 |  168741 |
 
 ## Contributing
 
diff --git a/poetry.lock b/poetry.lock
index ae0c01f..8d98bc4 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -13,13 +13,13 @@ files = [
 
 [[package]]
 name = "argcomplete"
-version = "3.2.2"
+version = "3.2.3"
 description = "Bash tab completion for argparse"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "argcomplete-3.2.2-py3-none-any.whl", hash = "sha256:e44f4e7985883ab3e73a103ef0acd27299dbfe2dfed00142c35d4ddd3005901d"},
-    {file = "argcomplete-3.2.2.tar.gz", hash = "sha256:f3e49e8ea59b4026ee29548e24488af46e30c9de57d48638e24f54a1ea1000a2"},
+    {file = "argcomplete-3.2.3-py3-none-any.whl", hash = "sha256:c12355e0494c76a2a7b73e3a59b09024ca0ba1e279fb9ed6c1b82d5b74b6a70c"},
+    {file = "argcomplete-3.2.3.tar.gz", hash = "sha256:bf7900329262e481be5a15f56f19736b376df6f82ed27576fa893652c5de6c23"},
 ]
 
 [package.extras]
@@ -313,13 +313,13 @@ files = [
 
 [[package]]
 name = "comm"
-version = "0.2.1"
+version = "0.2.2"
 description = "Jupyter Python Comm implementation, for usage in ipykernel, xeus-python etc."
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "comm-0.2.1-py3-none-any.whl", hash = "sha256:87928485c0dfc0e7976fd89fc1e187023cf587e7c353e4a9b417555b44adf021"},
-    {file = "comm-0.2.1.tar.gz", hash = "sha256:0bc91edae1344d39d3661dcbc36937181fdaddb304790458f8b044dbc064b89a"},
+    {file = "comm-0.2.2-py3-none-any.whl", hash = "sha256:e6fb86cb70ff661ee8c9c14e7d36d6de3b4066f1441be4063df9c5009f0a64d3"},
+    {file = "comm-0.2.2.tar.gz", hash = "sha256:3fd7a84065306e07bea1773df6eb8282de51ba82f77c72f9c85716ab11fe980e"},
 ]
 
 [package.dependencies]
@@ -330,13 +330,13 @@ test = ["pytest"]
 
 [[package]]
 name = "commitizen"
-version = "3.16.0"
+version = "3.18.4"
 description = "Python commitizen client tool"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "commitizen-3.16.0-py3-none-any.whl", hash = "sha256:a880005352fd35b908d9c3951e71e155b157f4a4ec61ca9c080a9637bf98e0a1"},
-    {file = "commitizen-3.16.0.tar.gz", hash = "sha256:1269619d383d12809f436ff196fb786a3d49fc50987562e6e566cd9c2908735c"},
+    {file = "commitizen-3.18.4-py3-none-any.whl", hash = "sha256:42c9b2c5fd3d6b83ebf850424227a8935d3e49f9fa636c58c072a370713b176a"},
+    {file = "commitizen-3.18.4.tar.gz", hash = "sha256:57b3051d4170e23a5317f348d1bc61b98e57ac01b04f66e0f9a25fef75e6f679"},
 ]
 
 [package.dependencies]
@@ -352,6 +352,69 @@ questionary = ">=2.0,<3.0"
 termcolor = ">=1.1,<3"
 tomlkit = ">=0.5.3,<1.0.0"
 
+[[package]]
+name = "contourpy"
+version = "1.2.0"
+description = "Python library for calculating contours of 2D quadrilateral grids"
+optional = false
+python-versions = ">=3.9"
+files = [
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 version = "2.6.0"
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 ]
 
 [package.dependencies]
@@ -514,6 +577,21 @@ ssh = ["bcrypt (>=3.1.5)"]
 test = ["certifi", "pretend", "pytest (>=6.2.0)", "pytest-benchmark", "pytest-cov", "pytest-xdist"]
 test-randomorder = ["pytest-randomly"]
 
+[[package]]
+name = "cycler"
+version = "0.12.1"
+description = "Composable style cycles"
+optional = false
+python-versions = ">=3.8"
+files = [
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+]
+
+[package.extras]
+docs = ["ipython", "matplotlib", "numpydoc", "sphinx"]
+tests = ["pytest", "pytest-cov", "pytest-xdist"]
+
 [[package]]
 name = "debugpy"
 version = "1.8.1"
@@ -657,6 +735,71 @@ docs = ["furo (>=2023.9.10)", "sphinx (>=7.2.6)", "sphinx-autodoc-typehints (>=1
 testing = ["covdefaults (>=2.3)", "coverage (>=7.3.2)", "diff-cover (>=8)", "pytest (>=7.4.3)", "pytest-cov (>=4.1)", "pytest-mock (>=3.12)", "pytest-timeout (>=2.2)"]
 typing = ["typing-extensions (>=4.8)"]
 
+[[package]]
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+version = "4.49.0"
+description = "Tools to manipulate font files"
+optional = false
+python-versions = ">=3.8"
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+]
+
+[package.extras]
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+graphite = ["lz4 (>=1.7.4.2)"]
+interpolatable = ["munkres", "pycairo", "scipy"]
+lxml = ["lxml (>=4.0)"]
+pathops = ["skia-pathops (>=0.5.0)"]
+plot = ["matplotlib"]
+repacker = ["uharfbuzz (>=0.23.0)"]
+symfont = ["sympy"]
+type1 = ["xattr"]
+ufo = ["fs (>=2.2.0,<3)"]
+unicode = ["unicodedata2 (>=15.1.0)"]
+woff = ["brotli (>=1.0.1)", "brotlicffi (>=0.8.0)", "zopfli (>=0.1.4)"]
+
 [[package]]
 name = "gitdb"
 version = "4.0.11"
@@ -715,22 +858,22 @@ files = [
 
 [[package]]
 name = "importlib-metadata"
-version = "7.0.1"
+version = "7.0.2"
 description = "Read metadata from Python packages"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "importlib_metadata-7.0.1-py3-none-any.whl", hash = "sha256:4805911c3a4ec7c3966410053e9ec6a1fecd629117df5adee56dfc9432a1081e"},
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+    {file = "importlib_metadata-7.0.2-py3-none-any.whl", hash = "sha256:f4bc4c0c070c490abf4ce96d715f68e95923320370efb66143df00199bb6c100"},
+    {file = "importlib_metadata-7.0.2.tar.gz", hash = "sha256:198f568f3230878cb1b44fbd7975f87906c22336dba2e4a7f05278c281fbd792"},
 ]
 
 [package.dependencies]
 zipp = ">=0.5"
 
 [package.extras]
-docs = ["furo", "jaraco.packaging (>=9.3)", "jaraco.tidelift (>=1.4)", "rst.linker (>=1.9)", "sphinx (<7.2.5)", "sphinx (>=3.5)", "sphinx-lint"]
+docs = ["furo", "jaraco.packaging (>=9.3)", "jaraco.tidelift (>=1.4)", "rst.linker (>=1.9)", "sphinx (>=3.5)", "sphinx-lint"]
 perf = ["ipython"]
-testing = ["flufl.flake8", "importlib-resources (>=1.3)", "packaging", "pyfakefs", "pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=2.2)", "pytest-mypy (>=0.9.1)", "pytest-perf (>=0.9.2)", "pytest-ruff"]
+testing = ["flufl.flake8", "importlib-resources (>=1.3)", "packaging", "pyfakefs", "pytest (>=6)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=2.2)", "pytest-mypy", "pytest-perf (>=0.9.2)", "pytest-ruff (>=0.2.1)"]
 
 [[package]]
 name = "iniconfig"
@@ -861,13 +1004,13 @@ files = [
 
 [[package]]
 name = "jupyter-client"
-version = "8.6.0"
+version = "8.6.1"
 description = "Jupyter protocol implementation and client libraries"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "jupyter_client-8.6.0-py3-none-any.whl", hash = "sha256:909c474dbe62582ae62b758bca86d6518c85234bdee2d908c778db6d72f39d99"},
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 ]
 
 [package.dependencies]
@@ -883,13 +1026,13 @@ test = ["coverage", "ipykernel (>=6.14)", "mypy", "paramiko", "pre-commit", "pyt
 
 [[package]]
 name = "jupyter-core"
-version = "5.7.1"
+version = "5.7.2"
 description = "Jupyter core package. A base package on which Jupyter projects rely."
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
@@ -899,7 +1042,120 @@ traitlets = ">=5.3"
 
 [package.extras]
 docs = ["myst-parser", "pydata-sphinx-theme", "sphinx-autodoc-typehints", "sphinxcontrib-github-alt", "sphinxcontrib-spelling", "traitlets"]
-test = ["ipykernel", "pre-commit", "pytest", "pytest-cov", "pytest-timeout"]
+test = ["ipykernel", "pre-commit", "pytest (<8)", "pytest-cov", "pytest-timeout"]
+
+[[package]]
+name = "kiwisolver"
+version = "1.4.5"
+description = "A fast implementation of the Cassowary constraint solver"
+optional = false
+python-versions = ">=3.7"
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 tests = ["pytest", "pytz", "simplejson"]
 
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 version = "0.1.6"
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+typing = ["typing-extensions"]
+xmp = ["defusedxml"]
+
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 version = "4.2.0"
@@ -1482,15 +1944,29 @@ files = [
 plugins = ["importlib-metadata"]
 windows-terminal = ["colorama (>=0.4.6)"]
 
+[[package]]
+name = "pyparsing"
+version = "3.1.2"
+description = "pyparsing module - Classes and methods to define and execute parsing grammars"
+optional = false
+python-versions = ">=3.6.8"
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+
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 iniconfig = "*"
 packaging = "*"
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 [package.extras]
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 name = "pytest-clarity"
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 [package.dependencies]
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 [package.extras]
 unidecode = ["Unidecode (>=1.1.1)"]
 
+[[package]]
+name = "pytz"
+version = "2024.1"
+description = "World timezone definitions, modern and historical"
+optional = false
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 [[package]]
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 version = "306"
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+    {file = "ruff-0.3.2.tar.gz", hash = "sha256:fa78ec9418eb1ca3db392811df3376b46471ae93792a81af2d1cbb0e5dcb5142"},
 ]
 
 [[package]]
@@ -2068,18 +2555,18 @@ test = ["asv", "gmpy2", "hypothesis", "mpmath", "pooch", "pytest", "pytest-cov",
 
 [[package]]
 name = "setuptools"
-version = "69.1.1"
+version = "69.2.0"
 description = "Easily download, build, install, upgrade, and uninstall Python packages"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "setuptools-69.1.1-py3-none-any.whl", hash = "sha256:02fa291a0471b3a18b2b2481ed902af520c69e8ae0919c13da936542754b4c56"},
-    {file = "setuptools-69.1.1.tar.gz", hash = "sha256:5c0806c7d9af348e6dd3777b4f4dbb42c7ad85b190104837488eab9a7c945cf8"},
+    {file = "setuptools-69.2.0-py3-none-any.whl", hash = "sha256:c21c49fb1042386df081cb5d86759792ab89efca84cf114889191cd09aacc80c"},
+    {file = "setuptools-69.2.0.tar.gz", hash = "sha256:0ff4183f8f42cd8fa3acea16c45205521a4ef28f73c6391d8a25e92893134f2e"},
 ]
 
 [package.extras]
 docs = ["furo", "jaraco.packaging (>=9.3)", "jaraco.tidelift (>=1.4)", "pygments-github-lexers (==0.0.5)", "rst.linker (>=1.9)", "sphinx (<7.2.5)", "sphinx (>=3.5)", "sphinx-favicon", "sphinx-inline-tabs", "sphinx-lint", "sphinx-notfound-page (>=1,<2)", "sphinx-reredirects", "sphinxcontrib-towncrier"]
-testing = ["build[virtualenv]", "filelock (>=3.4.0)", "flake8-2020", "ini2toml[lite] (>=0.9)", "jaraco.develop (>=7.21)", "jaraco.envs (>=2.2)", "jaraco.path (>=3.2.0)", "packaging (>=23.2)", "pip (>=19.1)", "pytest (>=6)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=2.2)", "pytest-home (>=0.5)", "pytest-mypy (>=0.9.1)", "pytest-perf", "pytest-ruff (>=0.2.1)", "pytest-timeout", "pytest-xdist", "tomli-w (>=1.0.0)", "virtualenv (>=13.0.0)", "wheel"]
+testing = ["build[virtualenv]", "filelock (>=3.4.0)", "importlib-metadata", "ini2toml[lite] (>=0.9)", "jaraco.develop (>=7.21)", "jaraco.envs (>=2.2)", "jaraco.path (>=3.2.0)", "mypy (==1.9)", "packaging (>=23.2)", "pip (>=19.1)", "pytest (>=6)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=2.2)", "pytest-home (>=0.5)", "pytest-mypy (>=0.9.1)", "pytest-perf", "pytest-ruff (>=0.2.1)", "pytest-timeout", "pytest-xdist (>=3)", "tomli", "tomli-w (>=1.0.0)", "virtualenv (>=13.0.0)", "wheel"]
 testing-integration = ["build[virtualenv] (>=1.0.3)", "filelock (>=3.4.0)", "jaraco.envs (>=2.2)", "jaraco.path (>=3.2.0)", "packaging (>=23.2)", "pytest", "pytest-enabler", "pytest-xdist", "tomli", "virtualenv (>=13.0.0)", "wheel"]
 
 [[package]]
@@ -2136,6 +2623,20 @@ pure-eval = "*"
 [package.extras]
 tests = ["cython", "littleutils", "pygments", "pytest", "typeguard"]
 
+[[package]]
+name = "tabulate"
+version = "0.9.0"
+description = "Pretty-print tabular data"
+optional = false
+python-versions = ">=3.7"
+files = [
+    {file = "tabulate-0.9.0-py3-none-any.whl", hash = "sha256:024ca478df22e9340661486f85298cff5f6dcdba14f3813e8830015b9ed1948f"},
+    {file = "tabulate-0.9.0.tar.gz", hash = "sha256:0095b12bf5966de529c0feb1fa08671671b3368eec77d7ef7ab114be2c068b3c"},
+]
+
+[package.extras]
+widechars = ["wcwidth"]
+
 [[package]]
 name = "termcolor"
 version = "2.4.0"
@@ -2216,36 +2717,18 @@ files = [
 
 [[package]]
 name = "traitlets"
-version = "5.14.1"
+version = "5.14.2"
 description = "Traitlets Python configuration system"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "traitlets-5.14.1-py3-none-any.whl", hash = "sha256:2e5a030e6eff91737c643231bfcf04a65b0132078dad75e4936700b213652e74"},
-    {file = "traitlets-5.14.1.tar.gz", hash = "sha256:8585105b371a04b8316a43d5ce29c098575c2e477850b62b848b964f1444527e"},
+    {file = "traitlets-5.14.2-py3-none-any.whl", hash = "sha256:fcdf85684a772ddeba87db2f398ce00b40ff550d1528c03c14dbf6a02003cd80"},
+    {file = "traitlets-5.14.2.tar.gz", hash = "sha256:8cdd83c040dab7d1dee822678e5f5d100b514f7b72b01615b26fc5718916fdf9"},
 ]
 
 [package.extras]
 docs = ["myst-parser", "pydata-sphinx-theme", "sphinx"]
-test = ["argcomplete (>=3.0.3)", "mypy (>=1.7.0)", "pre-commit", "pytest (>=7.0,<7.5)", "pytest-mock", "pytest-mypy-testing"]
-
-[[package]]
-name = "typeguard"
-version = "4.1.5"
-description = "Run-time type checker for Python"
-optional = false
-python-versions = ">=3.8"
-files = [
-    {file = "typeguard-4.1.5-py3-none-any.whl", hash = "sha256:8923e55f8873caec136c892c3bed1f676eae7be57cdb94819281b3d3bc9c0953"},
-    {file = "typeguard-4.1.5.tar.gz", hash = "sha256:ea0a113bbc111bcffc90789ebb215625c963411f7096a7e9062d4e4630c155fd"},
-]
-
-[package.dependencies]
-typing-extensions = {version = ">=4.7.0", markers = "python_version < \"3.12\""}
-
-[package.extras]
-doc = ["Sphinx (>=7)", "packaging", "sphinx-autodoc-typehints (>=1.2.0)"]
-test = ["coverage[toml] (>=7)", "mypy (>=1.2.0)", "pytest (>=7)"]
+test = ["argcomplete (>=3.0.3)", "mypy (>=1.7.0)", "pre-commit", "pytest (>=7.0,<8.1)", "pytest-mock", "pytest-mypy-testing"]
 
 [[package]]
 name = "typer"
@@ -2270,13 +2753,13 @@ test = ["black (>=22.3.0,<23.0.0)", "coverage (>=6.2,<7.0)", "isort (>=5.0.6,<6.
 
 [[package]]
 name = "types-python-dateutil"
-version = "2.8.19.20240106"
+version = "2.9.0.20240315"
 description = "Typing stubs for python-dateutil"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "types-python-dateutil-2.8.19.20240106.tar.gz", hash = "sha256:1f8db221c3b98e6ca02ea83a58371b22c374f42ae5bbdf186db9c9a76581459f"},
-    {file = "types_python_dateutil-2.8.19.20240106-py3-none-any.whl", hash = "sha256:efbbdc54590d0f16152fa103c9879c7d4a00e82078f6e2cf01769042165acaa2"},
+    {file = "types-python-dateutil-2.9.0.20240315.tar.gz", hash = "sha256:c1f6310088eb9585da1b9f811765b989ed2e2cdd4203c1a367e944b666507e4e"},
+    {file = "types_python_dateutil-2.9.0.20240315-py3-none-any.whl", hash = "sha256:78aa9124f360df90bb6e85eb1a4d06e75425445bf5ecb13774cb0adef7ff3956"},
 ]
 
 [[package]]
@@ -2290,6 +2773,17 @@ files = [
     {file = "typing_extensions-4.10.0.tar.gz", hash = "sha256:b0abd7c89e8fb96f98db18d86106ff1d90ab692004eb746cf6eda2682f91b3cb"},
 ]
 
+[[package]]
+name = "tzdata"
+version = "2024.1"
+description = "Provider of IANA time zone data"
+optional = false
+python-versions = ">=2"
+files = [
+    {file = "tzdata-2024.1-py2.py3-none-any.whl", hash = "sha256:9068bc196136463f5245e51efda838afa15aaeca9903f49050dfa2679db4d252"},
+    {file = "tzdata-2024.1.tar.gz", hash = "sha256:2674120f8d891909751c38abcdfd386ac0a5a1127954fbc332af6b5ceae07efd"},
+]
+
 [[package]]
 name = "urllib3"
 version = "2.2.1"
@@ -2338,22 +2832,49 @@ files = [
     {file = "wcwidth-0.2.13.tar.gz", hash = "sha256:72ea0c06399eb286d978fdedb6923a9eb47e1c486ce63e9b4e64fc18303972b5"},
 ]
 
+[[package]]
+name = "xgboost"
+version = "2.0.3"
+description = "XGBoost Python Package"
+optional = false
+python-versions = ">=3.8"
+files = [
+    {file = "xgboost-2.0.3-py3-none-macosx_10_15_x86_64.macosx_11_0_x86_64.macosx_12_0_x86_64.whl", hash = "sha256:b21b2bb188b162c615fce468db93e3f995f3690e6184aadc7743b58466dc7f13"},
+    {file = "xgboost-2.0.3-py3-none-macosx_12_0_arm64.whl", hash = "sha256:722d5b9351dfdf61973490dfd28abd42844db1cc469d07ed9b0cde9d1ffcdb32"},
+    {file = "xgboost-2.0.3-py3-none-manylinux2014_aarch64.whl", hash = "sha256:2315a57b1883221e2f78dd514559aa9797e6c272d995d22e45495a04adac93cc"},
+    {file = "xgboost-2.0.3-py3-none-manylinux2014_x86_64.whl", hash = "sha256:30bd5f789fad467fd49e04e5d19e04238b931682c3951a514da5c2410b3bf59c"},
+    {file = "xgboost-2.0.3-py3-none-win_amd64.whl", hash = "sha256:462f131d7bfb1bc42f67c57fa5aa3e57d2b5755b1573a6e0d2c7e8895164e0fc"},
+    {file = "xgboost-2.0.3.tar.gz", hash = "sha256:505955b5d770f8217a049beecce79e04a93787371c06dfb4b2414fec9d496bf3"},
+]
+
+[package.dependencies]
+numpy = "*"
+scipy = "*"
+
+[package.extras]
+dask = ["dask", "distributed", "pandas"]
+datatable = ["datatable"]
+pandas = ["pandas"]
+plotting = ["graphviz", "matplotlib"]
+pyspark = ["cloudpickle", "pyspark", "scikit-learn"]
+scikit-learn = ["scikit-learn"]
+
 [[package]]
 name = "zipp"
-version = "3.17.0"
+version = "3.18.1"
 description = "Backport of pathlib-compatible object wrapper for zip files"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "zipp-3.17.0-py3-none-any.whl", hash = "sha256:0e923e726174922dce09c53c59ad483ff7bbb8e572e00c7f7c46b88556409f31"},
-    {file = "zipp-3.17.0.tar.gz", hash = "sha256:84e64a1c28cf7e91ed2078bb8cc8c259cb19b76942096c8d7b84947690cabaf0"},
+    {file = "zipp-3.18.1-py3-none-any.whl", hash = "sha256:206f5a15f2af3dbaee80769fb7dc6f249695e940acca08dfb2a4769fe61e538b"},
+    {file = "zipp-3.18.1.tar.gz", hash = "sha256:2884ed22e7d8961de1c9a05142eb69a247f120291bc0206a00a7642f09b5b715"},
 ]
 
 [package.extras]
-docs = ["furo", "jaraco.packaging (>=9.3)", "jaraco.tidelift (>=1.4)", "rst.linker (>=1.9)", "sphinx (<7.2.5)", "sphinx (>=3.5)", "sphinx-lint"]
-testing = ["big-O", "jaraco.functools", "jaraco.itertools", "more-itertools", "pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=2.2)", "pytest-ignore-flaky", "pytest-mypy (>=0.9.1)", "pytest-ruff"]
+docs = ["furo", "jaraco.packaging (>=9.3)", "jaraco.tidelift (>=1.4)", "rst.linker (>=1.9)", "sphinx (>=3.5)", "sphinx-lint"]
+testing = ["big-O", "jaraco.functools", "jaraco.itertools", "more-itertools", "pytest (>=6)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=2.2)", "pytest-ignore-flaky", "pytest-mypy", "pytest-ruff (>=0.2.1)"]
 
 [metadata]
 lock-version = "2.0"
 python-versions = ">=3.10,<4.0"
-content-hash = "5947cbce669ff2c3d95aab095820c0e23d33536547f719ca000a709c6823e2d8"
+content-hash = "66395edcba74de2c62d2e0041e0844bfb4b8dfbd6f8dcb7097262b22f8d4ffec"
diff --git a/pyproject.toml b/pyproject.toml
index 81d38d0..8dbc797 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -18,13 +18,15 @@ version_provider = "poetry"
 
 [tool.poetry.dependencies]  # https://python-poetry.org/docs/dependency-specification/
 python = ">=3.10,<4.0"
-lightgbm = ">=4.0.0"
-scikit-learn = ">=1.1.0"
+scikit-learn = ">=1.0.0"
+xgboost = ">=2.0.0"
 
 [tool.poetry.group.test.dependencies]  # https://python-poetry.org/docs/master/managing-dependencies/
 commitizen = ">=3.2.1"
 coverage = { extras = ["toml"], version = ">=7.2.5" }
+lightgbm = ">=4.3.0"
 mypy = ">=1.2.0"
+pandas = ">=2.2.1"
 poethepoet = ">=0.20.0"
 pre-commit = ">=3.3.1"
 pytest = ">=7.3.1"
@@ -34,12 +36,13 @@ pytest-xdist = ">=3.2.1"
 ruff = ">=0.2.1"
 safety = ">=2.3.4,!=2.3.5"
 shellcheck-py = ">=0.9.0"
-typeguard = ">=3.0.2"
 
 [tool.poetry.group.dev.dependencies]  # https://python-poetry.org/docs/master/managing-dependencies/
 cruft = ">=2.14.0"
 ipykernel = ">=6.29.2"
+matplotlib = ">=3.8.3"
 pdoc = ">=13.1.1"
+tabulate = ">=0.9.0"
 
 [tool.coverage.report]  # https://coverage.readthedocs.io/en/latest/config.html#report
 fail_under = 50
@@ -69,7 +72,7 @@ show_error_context = true
 warn_unreachable = true
 
 [tool.pytest.ini_options]  # https://docs.pytest.org/en/latest/reference/reference.html#ini-options-ref
-addopts = "--color=yes --doctest-modules --exitfirst --failed-first --strict-config --strict-markers --typeguard-packages=conformal_tights --verbosity=2 --junitxml=reports/pytest.xml"
+addopts = "--color=yes --doctest-modules --exitfirst --failed-first --strict-config --strict-markers --verbosity=2 --junitxml=reports/pytest.xml"
 filterwarnings = ["error", "ignore::DeprecationWarning"]
 testpaths = ["src", "tests"]
 xfail_strict = true
@@ -83,7 +86,7 @@ target-version = "py310"
 [tool.ruff.lint]
 ignore-init-module-imports = true
 select = ["A", "ASYNC", "B", "BLE", "C4", "C90", "D", "DTZ", "E", "EM", "ERA", "F", "FBT", "FLY", "FURB", "G", "I", "ICN", "INP", "INT", "ISC", "LOG", "N", "NPY", "PERF", "PGH", "PIE", "PL", "PT", "PTH", "PYI", "Q", "RET", "RSE", "RUF", "S", "SIM", "SLF", "SLOT", "T10", "T20", "TCH", "TID", "TRY", "UP", "W", "YTT"]
-ignore = ["D203", "D213", "E501", "RET504", "S101", "S307"]
+ignore = ["D203", "D213", "E501", "N803", "N806", "RET504", "RUF002", "RUF003", "S101", "S307"]
 unfixable = ["ERA001", "F401", "F841", "T201", "T203"]
 
 [tool.ruff.lint.flake8-tidy-imports]
diff --git a/src/conformal_tights/__init__.py b/src/conformal_tights/__init__.py
index 58b5f3c..fb137d4 100644
--- a/src/conformal_tights/__init__.py
+++ b/src/conformal_tights/__init__.py
@@ -1 +1,7 @@
 """Conformal Tights package."""
+
+from conformal_tights._conformal_coherent_quantile_regressor import (
+    ConformalCoherentQuantileRegressor,
+)
+
+__all__ = ["ConformalCoherentQuantileRegressor"]
diff --git a/src/conformal_tights/_coherent_linear_quantile_regressor.py b/src/conformal_tights/_coherent_linear_quantile_regressor.py
new file mode 100644
index 0000000..7d37db2
--- /dev/null
+++ b/src/conformal_tights/_coherent_linear_quantile_regressor.py
@@ -0,0 +1,248 @@
+"""Coherent Linear Quantile Regressor."""
+
+from typing import TypeVar
+
+import numpy as np
+import numpy.typing as npt
+from scipy import sparse
+from scipy.optimize import linprog
+from scipy.sparse import csr_matrix
+from sklearn.base import BaseEstimator, RegressorMixin
+from sklearn.utils.validation import (
+    check_array,
+    check_consistent_length,
+    check_is_fitted,
+    check_X_y,
+)
+
+from conformal_tights._typing import FloatMatrix, FloatVector
+
+F = TypeVar("F", np.float32, np.float64)
+
+
+def coherent_linear_quantile_regression(
+    X: FloatMatrix[F],
+    y: FloatVector[F],
+    *,
+    quantiles: FloatVector[F],
+    sample_weight: FloatVector[F] | None = None,
+    coherence_buffer: int = 3,
+) -> FloatMatrix[F]:
+    """Solve a Coherent Linear Quantile Regression problem.
+
+    Minimizes the quantile loss:
+
+        ∑ᵢ,ⱼ {
+                 qⱼ (yᵢ - ŷ⁽ʲ⁾ᵢ) : yᵢ ≥ ŷ⁽ʲ⁾ᵢ,
+            (1 - qⱼ)(ŷ⁽ʲ⁾ᵢ - yᵢ) : ŷ⁽ʲ⁾ᵢ > yᵢ
+        }
+
+    for the linear model ŷ⁽ʲ⁾ := Xβ⁽ʲ⁾, given an input dataset X, target y, and quantile ranks qⱼ.
+
+    We achieve so-called 'coherent' quantiles by enforcing monotonicity of the predicted quantiles
+    with the constraint Xβ⁽ʲ⁾ ≤ Xβ⁽ʲ⁺¹⁾ for each consecutive pair of quantile ranks in an extended
+    set of quantile ranks that comprises the requested quantile ranks and a number of auxiliary
+    quantile ranks in between.
+
+    The optimization problem is formulated as a linear program by introducing the auxiliary residual
+    vectors Δ⁽ʲ⁾⁺, Δ⁽ʲ⁾⁻ ≥ 0 so that Xβ⁽ʲ⁾ - y = Δ⁽ʲ⁾⁺ - Δ⁽ʲ⁾⁻. The objective then becomes
+    ∑ᵢ,ⱼ qⱼΔ⁽ʲ⁾⁻ᵢ + (1 - qⱼ)Δ⁽ʲ⁾⁺ᵢ + αt⁽ʲ⁾ᵢ for t⁽ʲ⁾ := |β⁽ʲ⁾|. The L1 regularization parameter α is
+    automatically determined to minimize the impact on the solution β.
+
+    Parameters
+    ----------
+    X
+        The feature matrix.
+    y
+        The target values.
+    quantiles
+        The quantiles to estimate (between 0 and 1).
+    sample_weight
+        The optional sample weight to use for each sample.
+    coherence_buffer
+        The number of auxiliary quantiles to introduce. Smaller is faster, larger yields more
+        coherent quantiles.
+
+    Returns
+    -------
+    β
+        The estimated regression coefficients so that Xβ produces quantile predictions ŷ.
+    """
+    # Learn the input dimensions.
+    num_samples, num_features = X.shape
+    # Add buffer quantile ranks in between the given quantile ranks so that we have an even stronger
+    # guarantee on the monotonicity of the predicted quantiles.
+    quantiles = np.interp(
+        x=np.linspace(0, len(quantiles) - 1, (len(quantiles) - 1) * (1 + coherence_buffer) + 1),
+        xp=np.arange(len(quantiles)),
+        fp=quantiles,
+    ).astype(quantiles.dtype)
+    num_quantiles = len(quantiles)
+    # Validate the input.
+    assert np.array_equal(quantiles, np.sort(quantiles)), "Quantile ranks must be sorted."
+    assert sample_weight is None or np.all(sample_weight >= 0), "Sample weights must be >= 0."
+    # Normalise the sample weights.
+    sample_weight = np.ones(num_samples, dtype=y.dtype) if sample_weight is None else sample_weight
+    sample_weight /= np.sum(sample_weight)
+    eps = np.finfo(y.dtype).eps
+    α = np.sqrt(eps) / (num_quantiles * num_features)
+    # Construct the objective function ∑ᵢ,ⱼ qⱼΔ⁽ʲ⁾⁻ᵢ + (1 - qⱼ)Δ⁽ʲ⁾⁺ᵢ + αt⁽ʲ⁾ᵢ for t⁽ʲ⁾ := |β⁽ʲ⁾|.
+    c = np.hstack(
+        [
+            np.zeros(num_quantiles * num_features, dtype=y.dtype),  # β⁽ʲ⁾ for each qⱼ
+            α * np.ones(num_quantiles * num_features, dtype=y.dtype),  # t⁽ʲ⁾ for each qⱼ
+            np.kron((1 - quantiles) / num_quantiles, sample_weight),  # Δ⁽ʲ⁾⁺ for each qⱼ
+            np.kron(quantiles / num_quantiles, sample_weight),  # Δ⁽ʲ⁾⁻ for each qⱼ
+        ]
+    )
+    # Construct the equalities Xβ⁽ʲ⁾ - y = Δ⁽ʲ⁾⁺ - Δ⁽ʲ⁾⁻ for each quantile rank qⱼ.
+    A_eq = sparse.hstack(
+        [
+            # Xβ⁽ʲ⁾ for each qⱼ (block diagonal matrix)
+            sparse.kron(sparse.eye(num_quantiles, dtype=X.dtype), X),
+            # t⁽ʲ⁾ not used in this constraint
+            csr_matrix((num_quantiles * num_samples, num_quantiles * num_features), dtype=X.dtype),
+            # -Δ⁽ʲ⁾⁺ for each qⱼ (block diagonal matrix)
+            -sparse.eye(num_quantiles * num_samples, dtype=X.dtype),
+            # Δ⁽ʲ⁾⁻ for each qⱼ (block diagonal matrix)
+            sparse.eye(num_quantiles * num_samples, dtype=X.dtype),
+        ]
+    )
+    b_eq = np.tile(y, num_quantiles)
+    # Construct the inequalities -t⁽ʲ⁾ <= β⁽ʲ⁾ <= t⁽ʲ⁾ for each quantile rank qⱼ so that
+    # t⁽ʲ⁾ := |β⁽ʲ⁾|. Also construct the monotonicity constraint Xβ⁽ʲ⁾ <= Xβ⁽ʲ⁺¹⁾ for each qⱼ,
+    # equivalent to Δ⁽ʲ⁾⁺ - Δ⁽ʲ⁾⁻ <= Δ⁽ʲ⁺¹⁾⁺ - Δ⁽ʲ⁺¹⁾⁻.
+    zeros_Δ = csr_matrix(
+        (num_quantiles * num_features, 2 * num_quantiles * num_samples), dtype=X.dtype
+    )
+    zeros_βt = csr_matrix(
+        ((num_quantiles - 1) * num_samples, 2 * num_quantiles * num_features), dtype=X.dtype
+    )
+    A_ub = sparse.vstack(
+        [
+            sparse.hstack(
+                [
+                    sparse.eye(num_quantiles * num_features, dtype=X.dtype),  # β⁽ʲ⁾
+                    -sparse.eye(num_quantiles * num_features, dtype=X.dtype),  # -t⁽ʲ⁾
+                    zeros_Δ,  # Δ⁽ʲ⁾⁺ and Δ⁽ʲ⁾⁺ not used for this constraint
+                ]
+            ),
+            sparse.hstack(
+                [
+                    -sparse.eye(num_quantiles * num_features, dtype=X.dtype),  # -β⁽ʲ⁾
+                    -sparse.eye(num_quantiles * num_features, dtype=X.dtype),  # -t⁽ʲ⁾
+                    zeros_Δ,  # Δ⁽ʲ⁾⁺ and Δ⁽ʲ⁾⁺ not used for this constraint
+                ]
+            ),
+            sparse.hstack(
+                [
+                    zeros_βt,
+                    sparse.kron(
+                        sparse.diags(
+                            diagonals=[1, -1],  # Δ⁽ʲ⁾⁺ - Δ⁽ʲ⁺¹⁾⁺
+                            offsets=[0, 1],
+                            shape=(num_quantiles - 1, num_quantiles),
+                            dtype=X.dtype,
+                        ),
+                        sparse.eye(num_samples, dtype=X.dtype),
+                    ),
+                    sparse.kron(
+                        sparse.diags(
+                            diagonals=[-1, 1],  # -Δ⁽ʲ⁾⁻ + Δ⁽ʲ⁺¹⁾⁻
+                            offsets=[0, 1],
+                            shape=(num_quantiles - 1, num_quantiles),
+                            dtype=X.dtype,
+                        ),
+                        sparse.eye(num_samples, dtype=X.dtype),
+                    ),
+                ]
+            ),
+        ]
+    )
+    b_ub = np.zeros(A_ub.shape[0], dtype=X.dtype)
+    # Construct the bounds.
+    bounds = (
+        ([(None, None)] * num_quantiles * num_features)  # β⁽ʲ⁾ for each qⱼ
+        + ([(0, None)] * num_quantiles * num_features)  # t⁽ʲ⁾ for each qⱼ
+        + ([(0, None)] * num_quantiles * num_samples)  # Δ⁽ʲ⁾⁺ for each qⱼ
+        + ([(0, None)] * num_quantiles * num_samples)  # Δ⁽ʲ⁾⁻ for each qⱼ
+    )
+    # Solve the Coherent Quantile Regression LP.
+    result = linprog(c=c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, bounds=bounds, method="highs")
+    # Extract the solution.
+    β: FloatVector[F] = result.x[: num_quantiles * num_features].astype(y.dtype)
+    β = β.reshape(num_quantiles, num_features).T
+    β = β[:, 0 :: (coherence_buffer + 1)]  # Drop the buffer quantile ranks we introduced earlier.
+    return β
+
+
+class CoherentLinearQuantileRegressor(RegressorMixin, BaseEstimator):
+    """Coherent Linear Quantile Regressor.
+
+    A linear model that regresses multiple quantiles coherently so that the predicted quantiles for
+    a given example increase monotonically.
+    """
+
+    def __init__(
+        self,
+        *,
+        quantiles: npt.ArrayLike = (0.025, 0.5, 0.975),
+        fit_intercept: bool = True,
+        coherence_buffer: int = 3,
+    ) -> None:
+        """Initialize the Coherent Quantile Regressor.
+
+        Parameters
+        ----------
+        quantiles
+            The target quantiles to fit and predict.
+        fit_intercept
+            Whether to fit an intercept term.
+        coherence_buffer
+            The number of auxiliary quantiles to introduce. Smaller is faster, larger yields more
+            coherent quantiles.
+        """
+        self.quantiles = quantiles
+        self.fit_intercept = fit_intercept
+        self.coherence_buffer = coherence_buffer
+
+    def fit(
+        self, X: FloatMatrix[F], y: FloatVector[F], *, sample_weight: FloatVector[F] | None = None
+    ) -> "CoherentLinearQuantileRegressor":
+        """Fit this predictor."""
+        # Validate input.
+        X, y = check_X_y(X, y, y_numeric=True)
+        self.n_features_in_: int = X.shape[1]
+        self.y_dtype_: npt.DTypeLike = y.dtype  # Used to cast predictions to the correct dtype.
+        if np.all(y.astype(np.intp) == y):
+            self.y_dtype_ = np.intp  # To satisfy sklearn's `check_regressors_int`.
+        y = y.astype(np.float64)  # To support datetime64[ns] and timedelta64[ns].
+        if sample_weight is not None:
+            check_consistent_length(y, sample_weight)
+            sample_weight = np.asarray(sample_weight).astype(np.float64)
+        # Add a constant column to X to allow for a bias in the regression.
+        if self.fit_intercept:
+            X = np.hstack([X, np.ones((X.shape[0], 1), dtype=X.dtype)])
+        # Fit the coherent quantile regression model.
+        self.β_ = coherent_linear_quantile_regression(
+            X,
+            y,
+            quantiles=np.asarray(self.quantiles),
+            sample_weight=sample_weight,
+            coherence_buffer=self.coherence_buffer,
+        )
+        return self
+
+    def predict(self, X: FloatMatrix[F]) -> FloatMatrix[F]:
+        """Predict the output on a given dataset."""
+        # Check input.
+        check_is_fitted(self)
+        X = check_array(X)
+        # Add a constant column to X to allow for a bias in the regression.
+        if self.fit_intercept:
+            X = np.hstack([X, np.ones((X.shape[0], 1), dtype=X.dtype)])
+        # Predict the output.
+        ŷ: FloatMatrix[F] = X @ self.β_
+        # Map back to the training target dtype.
+        ŷ = np.squeeze(ŷ.astype(self.y_dtype_), axis=1 if ŷ.shape[1] == 1 else ())
+        return ŷ
diff --git a/src/conformal_tights/_conformal_coherent_quantile_regressor.py b/src/conformal_tights/_conformal_coherent_quantile_regressor.py
new file mode 100644
index 0000000..e145cfe
--- /dev/null
+++ b/src/conformal_tights/_conformal_coherent_quantile_regressor.py
@@ -0,0 +1,359 @@
+"""Conformal Coherent Quantile Regressor meta-estimator."""
+
+from typing import TYPE_CHECKING, Literal, TypeVar, overload
+
+import numpy as np
+import numpy.typing as npt
+from sklearn.base import BaseEstimator, MetaEstimatorMixin, RegressorMixin, clone
+from sklearn.model_selection import train_test_split
+from sklearn.utils.validation import (
+    check_array,
+    check_consistent_length,
+    check_is_fitted,
+    check_X_y,
+)
+from xgboost import XGBRegressor
+
+from conformal_tights._coherent_linear_quantile_regressor import CoherentLinearQuantileRegressor
+from conformal_tights._typing import FloatMatrix, FloatVector
+
+if TYPE_CHECKING:
+    import pandas as pd
+
+F = TypeVar("F", np.float32, np.float64)
+
+
+class ConformalCoherentQuantileRegressor(MetaEstimatorMixin, RegressorMixin, BaseEstimator):
+    """Conformal Coherent Quantile Regressor meta-estimator.
+
+    Adds conformally calibrated quantile and interval prediction to a given regressor by fitting a
+    meta-estimator as follows:
+
+        1. The given data is split into a training set and a conformal calibration set.
+        2. The training set is used to fit the given regressor.
+        3. The training set is also used to fit a nonconformity estimator, which is by default an
+           XGBoost vector quantile regressor for the quantiles (1/8, 1/4, 1/2, 3/4, 7/8). These
+           quantiles are not necessarily monotonic and may cross each other.
+        4. The conformal calibration set is split into two levels.
+        5. The level 1 conformal calibration set is used to fit a Coherent Linear Quantile
+           Regression model of the (relative) residuals given the level 1 nonconformity estimates.
+           This model produces conformally calibrated quantiles of the (relative) residuals that are
+           coherent in the sense that they increase monotonically.
+        6. The level 2 conformal calibration set is used to fit a per-quantile conformal bias on top
+           of the level 1 conformal quantile predictions of the (relative) residuals.
+
+    Quantile and interval predictions are made by predicting the nonconformity estimates, converting
+    those into conformally calibrated and coherent quantiles, and then adding a conformally
+    calibrated bias to the result. At the user's request, the bias can prioritize quantile accuracy
+    or interval coverage.
+
+    The level 1 and level 2 conformal predictors are lazily fitted on both the absolute and relative
+    residuals for the requested quantiles at prediction time. This allows the user to choose which
+    quantiles to predict, and to select the quantile predictions with the lowest dispersion.
+    """
+
+    def __init__(  # noqa: PLR0913
+        self,
+        estimator: BaseEstimator | Literal["auto"] = "auto",
+        *,
+        nonconformity_estimator: BaseEstimator | Literal["auto"] = "auto",
+        nonconformity_quantiles: npt.ArrayLike = (1 / 8, 1 / 4, 1 / 2, 3 / 4, 7 / 8),
+        conformal_calibration_size: tuple[float, int] = (0.3, 1440),
+        random_state: int | np.random.RandomState | None = 42,
+    ) -> None:
+        """Initialize the Conformal Coherent Quantile Regressor.
+
+        Parameters
+        ----------
+        estimator
+            The regressor to wrap, used for point prediction. If "auto", uses an `XGBRegressor`.
+        nonconformity_estimator
+            A nonconformity estimator to use. If "auto", uses XGBoost's vector quantile regressor
+            for the given `nonconformity_quantiles`.
+        nonconformity_quantiles
+            The quantiles that the nonconformity estimator should predict when
+            `nonconformity_estimator` is "auto".
+        conformal_calibration_size
+            A tuple of the relative and absolute size of the conformal calibration set. The smallest
+            of the two is used.
+        random_state
+            The random state to use for reproducibility.
+        """
+        self.estimator = estimator
+        self.nonconformity_estimator = nonconformity_estimator
+        self.nonconformity_quantiles = nonconformity_quantiles
+        self.conformal_calibration_size = conformal_calibration_size
+        self.random_state = random_state
+
+    def fit(
+        self,
+        X: "FloatMatrix[F] | pd.DataFrame",
+        y: "FloatVector[F] | pd.Series",
+        *,
+        sample_weight: "FloatVector[F] | pd.Series | None" = None,
+    ) -> "ConformalCoherentQuantileRegressor":
+        """Fit this predictor."""
+        # Validate input.
+        check_X_y(X, y, force_all_finite=False, ensure_min_samples=3, y_numeric=True)
+        # Learn dimensionality and dtypes.
+        if not hasattr(X, "dtypes"):
+            X = np.asarray(X)
+        y = np.ravel(np.asarray(y))
+        self.n_features_in_: int = X.shape[1]
+        self.y_dtype_: npt.DTypeLike = y.dtype  # Used to cast predictions to the correct dtype.
+        if np.all(y.astype(np.intp) == y):
+            self.y_dtype_ = np.intp  # To satisfy sklearn's `check_regressors_int`.
+        y = y.astype(np.float64)  # To support datetime64[ns] and timedelta64[ns].
+        if sample_weight is not None:
+            check_consistent_length(y, sample_weight)
+            sample_weight = np.ravel(np.asarray(sample_weight).astype(np.float64))
+        # Use the smallest of the relative and absolute calibration sizes.
+        calib_size = min(
+            int(self.conformal_calibration_size[0] * X.shape[0]), self.conformal_calibration_size[1]
+        )
+        # Split input into training and conformal calibration sets.
+        X_train, self.X_calib_, y_train, self.y_calib_, *sample_weights = train_test_split(
+            X,
+            y,
+            *([sample_weight] if sample_weight is not None else []),
+            test_size=calib_size,
+            random_state=self.random_state,
+        )
+        sample_weight_train, sample_weight_calib = (
+            sample_weights[:2] if sample_weight is not None else (None, None)
+        )
+        # Split the conformal calibration set into two levels.
+        X_calib_l1, X_calib_l2, y_calib_l1, y_calib_l2, *sample_weights_calib = train_test_split(
+            self.X_calib_,
+            self.y_calib_,
+            *([sample_weight_calib] if sample_weight_calib is not None else []),
+            test_size=self.conformal_calibration_size[0],
+            random_state=self.random_state,
+        )
+        self.sample_weight_calib_l1_, self.sample_weight_calib_l2_ = (
+            sample_weights_calib[:2] if sample_weight is not None else (None, None)  # type: ignore[has-type]
+        )
+        # Fit the given estimator on the training data.
+        self.estimator_ = (
+            clone(self.estimator)
+            if self.estimator != "auto"
+            else XGBRegressor(objective="reg:absoluteerror")
+        )
+        if isinstance(self.estimator_, XGBRegressor):
+            self.estimator_.set_params(enable_categorical=True, random_state=self.random_state)
+        self.estimator_.fit(X_train, y_train, sample_weight=sample_weight_train)
+        # Fit a nonconformity estimator on the training data with XGBRegressor's vector quantile
+        # regression. We fit a minimal number of quantiles to reduce the computational cost, but
+        # also to reduce the risk of overfitting in the coherent quantile regressor that is applied
+        # on top of the nonconformity estimates.
+        self.nonconformity_estimator_ = (
+            clone(self.nonconformity_estimator)
+            if self.nonconformity_estimator != "auto"
+            else XGBRegressor()
+        )
+        if isinstance(self.nonconformity_estimator_, XGBRegressor):
+            self.nonconformity_estimator_.set_params(
+                objective="reg:quantileerror",
+                quantile_alpha=self.nonconformity_quantiles,
+                enable_categorical=True,
+                random_state=self.random_state,
+            )
+        self.nonconformity_estimator_.fit(X_train, y_train, sample_weight=sample_weight_train)
+        # Predict on the level 1 calibration set.
+        self.ŷ_calib_l1_ = self.estimator_.predict(X_calib_l1)
+        self.ŷ_calib_l1_nonconformity_ = self.nonconformity_estimator_.predict(X_calib_l1)
+        self.residuals_calib_l1_ = self.ŷ_calib_l1_ - y_calib_l1
+        # Predict on the level 2 calibration set.
+        self.ŷ_calib_l2_ = self.estimator_.predict(X_calib_l2)
+        self.ŷ_calib_l2_nonconformity_ = self.nonconformity_estimator_.predict(X_calib_l2)
+        self.residuals_calib_l2_ = self.ŷ_calib_l2_ - y_calib_l2
+        # Lazily fit level 1 conformal predictors as coherent linear quantile regression models that
+        # predict quantiles of the (relative) residuals given the nonconformity estimates, and
+        # level 2 conformal biases.
+        self.conformal_l1_: dict[str, dict[tuple[float, ...], CoherentLinearQuantileRegressor]] = {
+            "Δŷ": {},
+            "Δŷ/ŷ": {},
+        }
+        self.conformal_l2_: dict[str, dict[tuple[float, ...], FloatVector[F]]] = {
+            "Δŷ": {},
+            "Δŷ/ŷ": {},
+        }
+        return self
+
+    def _lazily_fit_conformal_predictor(
+        self, target_type: str, quantiles: npt.ArrayLike
+    ) -> tuple[CoherentLinearQuantileRegressor, FloatVector[F]]:
+        """Lazily fit a conformal predictor for a given array of quantiles."""
+        quantiles = np.asarray(quantiles)
+        quantiles_tuple = tuple(quantiles)
+        if quantiles_tuple in self.conformal_l1_[target_type]:
+            # Retrieve level 1 and level 2.
+            cqr_l1 = self.conformal_l1_[target_type][quantiles_tuple]
+            bias_l2 = self.conformal_l2_[target_type][quantiles_tuple]
+        else:
+            # Fit level 1: a coherent quantile regressor that predicts quantiles of the (relative)
+            # residuals.
+            eps = np.finfo(self.ŷ_calib_l1_.dtype).eps
+            abs_ŷ_calib_l1 = np.maximum(np.abs(self.ŷ_calib_l1_), eps)
+            X_cqr = self.ŷ_calib_l1_nonconformity_
+            y_cqr = self.residuals_calib_l1_ / (abs_ŷ_calib_l1 if "/ŷ" in target_type else 1)
+            cqr_l1 = CoherentLinearQuantileRegressor(quantiles=quantiles)
+            cqr_l1.fit(X_cqr, y_cqr, sample_weight=self.sample_weight_calib_l1_)
+            self.conformal_l1_[target_type][quantiles_tuple] = cqr_l1
+            # Fit level 2: a per-quantile conformal bias on top of the level 1 conformal quantile
+            # predictions of the (relative) residuals.
+            abs_ŷ_calib_l2 = np.maximum(np.abs(self.ŷ_calib_l2_), eps)
+            Δŷ_calib_l2_quantiles = cqr_l1.predict(self.ŷ_calib_l2_nonconformity_)
+            bias_l2 = np.empty(quantiles.shape, dtype=self.ŷ_calib_l1_.dtype)
+            for j, quantile in enumerate(quantiles):
+                bias_l2[j] = np.quantile(
+                    -(
+                        (self.residuals_calib_l2_ / (abs_ŷ_calib_l2 if "/ŷ" in target_type else 1))
+                        + Δŷ_calib_l2_quantiles[:, j]
+                    ),
+                    quantile,
+                )
+            self.conformal_l2_[target_type][quantiles_tuple] = bias_l2
+        return cqr_l1, bias_l2  # type: ignore[return-value]
+
+    @overload
+    def predict_quantiles(
+        self,
+        X: FloatMatrix[F],
+        *,
+        quantiles: npt.ArrayLike,
+        priority: Literal["accuracy", "coverage"] = "accuracy",
+    ) -> FloatMatrix[F]: ...
+
+    @overload
+    def predict_quantiles(
+        self,
+        X: "pd.DataFrame",
+        *,
+        quantiles: npt.ArrayLike,
+        priority: Literal["accuracy", "coverage"] = "accuracy",
+    ) -> "pd.DataFrame": ...
+
+    def predict_quantiles(
+        self,
+        X: "FloatMatrix[F] | pd.DataFrame",
+        *,
+        quantiles: npt.ArrayLike,
+        priority: Literal["accuracy", "coverage"] = "accuracy",
+    ) -> "FloatMatrix[F] | pd.DataFrame":
+        """Predict conformally calibrated quantiles on a given dataset."""
+        # Predict the absolute and relative quantiles.
+        quantiles = np.asarray(quantiles)
+        ŷ = np.asarray(self.estimator_.predict(X))
+        X_cqr = self.nonconformity_estimator_.predict(X)
+        cqr_abs, bias_abs = self._lazily_fit_conformal_predictor("Δŷ", quantiles)
+        cqr_rel, bias_rel = self._lazily_fit_conformal_predictor("Δŷ/ŷ", quantiles)
+        if priority == "coverage":  # Only allow quantile expansion when the priority is coverage.
+            center = 0.5
+            bias_abs[center <= quantiles] = np.maximum(bias_abs[center <= quantiles], 0)
+            bias_abs[quantiles <= center] = np.minimum(bias_abs[quantiles <= center], 0)
+            bias_rel[center <= quantiles] = np.maximum(bias_rel[center <= quantiles], 0)
+            bias_rel[quantiles <= center] = np.minimum(bias_rel[quantiles <= center], 0)
+        Δŷ_quantiles = np.dstack(
+            [
+                cqr_abs.predict(X_cqr) + bias_abs[np.newaxis, :],
+                np.abs(ŷ[:, np.newaxis]) * (cqr_rel.predict(X_cqr) + bias_rel[np.newaxis, :]),
+            ]
+        )
+        # Choose between the the absolute and relative quantiles for each example in order to
+        # minimise the dispersion of the predicted quantiles.
+        dispersion = np.std(Δŷ_quantiles, axis=1)
+        Δŷ_quantiles = Δŷ_quantiles[
+            np.arange(Δŷ_quantiles.shape[0]), :, np.argmin(dispersion, axis=-1)
+        ]
+        ŷ_quantiles: FloatMatrix[F] = (ŷ[:, np.newaxis] + Δŷ_quantiles).astype(self.y_dtype_)
+        # Convert ŷ_quantiles to a pandas DataFrame if X is a pandas DataFrame.
+        if hasattr(X, "dtypes") and hasattr(X, "index"):
+            try:
+                import pandas as pd
+            except ImportError:
+                pass
+            else:
+                ŷ_quantiles_df = pd.DataFrame(ŷ_quantiles, index=X.index, columns=quantiles)
+                ŷ_quantiles_df.columns.name = "quantiles"
+                return ŷ_quantiles_df
+        return ŷ_quantiles
+
+    @overload
+    def predict_interval(self, X: FloatMatrix[F], *, coverage: float = 0.95) -> FloatMatrix[F]: ...
+
+    @overload
+    def predict_interval(self, X: "pd.DataFrame", *, coverage: float = 0.95) -> "pd.DataFrame": ...
+
+    def predict_interval(
+        self, X: "FloatMatrix[F] | pd.DataFrame", *, coverage: float = 0.95
+    ) -> "FloatMatrix[F] | pd.DataFrame":
+        """Predict conformally calibrated intervals on a given dataset."""
+        # Convert the coverage probability to lower and upper quantiles.
+        lb = (1 - coverage) / 2
+        ub = 1 - lb
+        # Compute the prediction interval with predict_quantiles.
+        ŷ_quantiles = self.predict_quantiles(X, quantiles=(lb, ub), priority="coverage")
+        return ŷ_quantiles
+
+    @overload
+    def predict(
+        self, X: FloatMatrix[F], *, coverage: None = None, quantiles: None = None
+    ) -> FloatVector[F]: ...
+
+    @overload
+    def predict(
+        self, X: FloatMatrix[F], *, coverage: float, quantiles: None = None
+    ) -> FloatMatrix[F]: ...
+
+    @overload
+    def predict(
+        self, X: FloatMatrix[F], *, coverage: None = None, quantiles: npt.ArrayLike
+    ) -> FloatMatrix[F]: ...
+
+    @overload
+    def predict(
+        self, X: "pd.DataFrame", *, coverage: None = None, quantiles: None = None
+    ) -> "pd.Series": ...
+
+    @overload
+    def predict(
+        self, X: "pd.DataFrame", *, coverage: float, quantiles: None = None
+    ) -> "pd.DataFrame": ...
+
+    @overload
+    def predict(
+        self, X: "pd.DataFrame", *, coverage: None = None, quantiles: npt.ArrayLike
+    ) -> "pd.DataFrame": ...
+
+    def predict(
+        self,
+        X: "FloatMatrix[F] | pd.DataFrame",
+        *,
+        coverage: float | None = None,
+        quantiles: npt.ArrayLike | None = None,
+    ) -> "FloatVector[F] | pd.Series | FloatMatrix[F] | pd.DataFrame":
+        """Predict on a given dataset."""
+        assert coverage is None or quantiles is None
+        check_is_fitted(self)
+        check_array(X, force_all_finite=False)
+        if coverage is not None:
+            ŷ_interval = self.predict_interval(X, coverage=coverage)
+            return ŷ_interval
+        if quantiles is not None:
+            ŷ_quantiles = self.predict_quantiles(X, quantiles=quantiles)
+            return ŷ_quantiles
+        ŷ = self.estimator_.predict(X).astype(self.y_dtype_)
+        if hasattr(X, "dtypes") and hasattr(X, "index"):
+            try:
+                import pandas as pd
+            except ImportError:
+                pass
+            else:
+                ŷ_series = pd.Series(ŷ, index=X.index)
+                return ŷ_series
+        return ŷ
+
+    def _more_tags(self) -> dict[str, bool]:
+        """Return more tags for the estimator."""
+        return {"allow_nan": True}
diff --git a/src/conformal_tights/_typing.py b/src/conformal_tights/_typing.py
new file mode 100644
index 0000000..efe6f4b
--- /dev/null
+++ b/src/conformal_tights/_typing.py
@@ -0,0 +1,11 @@
+"""Conformal Tights types."""
+
+from typing import TypeAlias, TypeVar
+
+import numpy as np
+import numpy.typing as npt
+
+F = TypeVar("F", np.float32, np.float64)
+
+FloatVector: TypeAlias = npt.NDArray[F]
+FloatMatrix: TypeAlias = npt.NDArray[F]
diff --git a/tests/conftest.py b/tests/conftest.py
new file mode 100644
index 0000000..5954bcd
--- /dev/null
+++ b/tests/conftest.py
@@ -0,0 +1,34 @@
+"""Test fixtures."""
+
+from typing import TypeAlias
+
+import pandas as pd
+import pytest
+import sklearn.datasets
+from _pytest.fixtures import SubRequest
+from sklearn.model_selection import train_test_split
+
+Dataset: TypeAlias = tuple[pd.DataFrame, pd.DataFrame, pd.Series, pd.Series]
+
+
+@pytest.fixture(
+    params=[
+        pytest.param(
+            43926,
+            id="dataset:ames_housing",  # Regression
+        ),
+        pytest.param(
+            287,
+            id="dataset:wine_quality",  # Regression
+        ),
+    ],
+)
+def dataset(request: SubRequest) -> Dataset:
+    """Train and test dataset fixture."""
+    # Download the dataset.
+    X, y = sklearn.datasets.fetch_openml(
+        data_id=request.param, return_X_y=True, as_frame=True, parser="auto"
+    )
+    # Split in train and test set.
+    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.15, random_state=42)
+    return X_train, X_test, y_train, y_test
diff --git a/tests/test_coherent_linear_quantile_regressor.py b/tests/test_coherent_linear_quantile_regressor.py
new file mode 100644
index 0000000..66fca27
--- /dev/null
+++ b/tests/test_coherent_linear_quantile_regressor.py
@@ -0,0 +1,16 @@
+"""Test the Coherent Linear Quantile Regressor."""
+
+import os
+
+import numpy as np
+import pytest
+from sklearn.utils.estimator_checks import check_estimator
+
+from conformal_tights._coherent_linear_quantile_regressor import CoherentLinearQuantileRegressor
+
+
+@pytest.mark.skipif(os.getenv("CI") == "true", reason="Skip on GitHub Actions")
+def test_sklearn_check_estimator() -> None:
+    """Check that the meta-estimator conforms to sklearn's standards."""
+    model = CoherentLinearQuantileRegressor(quantiles=np.array([0.5]))
+    check_estimator(model)
diff --git a/tests/test_conformal_quantile_regressor.py b/tests/test_conformal_quantile_regressor.py
new file mode 100644
index 0000000..753dd1e
--- /dev/null
+++ b/tests/test_conformal_quantile_regressor.py
@@ -0,0 +1,49 @@
+"""Test the Conformal Coherent Quantile Regressor."""
+
+import numpy as np
+import pytest
+from _pytest.fixtures import SubRequest
+from lightgbm import LGBMRegressor
+from sklearn.base import BaseEstimator
+from sklearn.utils.estimator_checks import check_estimator
+from xgboost import XGBRegressor
+
+from conformal_tights import ConformalCoherentQuantileRegressor
+from tests.conftest import Dataset
+
+
+@pytest.fixture(
+    params=[
+        pytest.param(XGBRegressor(objective="reg:absoluteerror"), id="model:XGBRegressor"),
+        pytest.param(LGBMRegressor(objective="regression_l1"), id="model:LGBMRegressor"),
+    ]
+)
+def regressor(request: SubRequest) -> BaseEstimator:
+    """Return a regressor."""
+    return request.param
+
+
+def test_conformal_quantile_regressor_coverage(dataset: Dataset, regressor: BaseEstimator) -> None:
+    """Test ConformalCoherentQuantileRegressor's coverage."""
+    # Unpack the dataset.
+    X_train, X_test, y_train, y_test = dataset
+    # Train the models.
+    model = ConformalCoherentQuantileRegressor(estimator=regressor)
+    model.fit(X_train, y_train)
+    # Verify the coherence of the predicted quantiles.
+    ŷ_quantiles = model.predict(X_test, quantiles=np.linspace(0.1, 0.9, 3))
+    for i in range(ŷ_quantiles.shape[1] - 1):
+        assert np.all(ŷ_quantiles.iloc[:, i] <= ŷ_quantiles.iloc[:, i + 1])
+    # Verify the coverage of the predicted intervals.
+    for desired_coverage in (0.7, 0.8, 0.9):
+        ŷ_interval = model.predict(X_test, coverage=desired_coverage)
+        assert np.all(ŷ_interval.iloc[:, 0] <= ŷ_interval.iloc[:, 1])
+        covered = (ŷ_interval.iloc[:, 0] <= y_test) & (y_test <= ŷ_interval.iloc[:, 1])
+        actual_coverage = np.mean(covered)
+        assert actual_coverage >= 0.97 * desired_coverage
+
+
+def test_sklearn_check_estimator() -> None:
+    """Check that the meta-estimator conforms to sklearn's standards."""
+    model = ConformalCoherentQuantileRegressor(estimator=XGBRegressor())
+    check_estimator(model)