DyadicKDE.jl

Dyadic kernel density estimation in Julia.

Introduction

This repository provides a Julia package which implements the methods for dyadic kernel density estimation detailed in Cattaneo, Feng and Underwood, 2022. In particular, the package provides the capability for computing

• Point estimates of a univariate dyadic density function
• Pointwise confidence intervals for the density
• Bonferroni-corrected confidence intervals
• Uniform confidence bands
• A rule-of-thumb bandwidth selector
• Counterfactual dyadic density estimation

The currently supported kernels are

• Epanechnikov, order 2
• Epanechnikov, order 4

Installation

Install from the Julia General registry by starting a Julia interactive session and running

] add DyadicKDE

Alternatively install from source by running

] add "https://github.com/WGUNDERWOOD/DyadicKDE.jl.git"

The package can then be loaded with

using DyadicKDE

and tested (this may take a few minutes) with

] test DyadicKDE

Dependencies

DyadicKDE.jl requires Julia 1.x and depends on several other Julia packages listed in Project.toml.

Quick start guide

# load package
using DyadicKDE

# specify parameters
n_data = 100
kernel_name = "epanechnikov_order_2"
evals = collect(range(-2.0, stop=2.0, length=10))
sdp_solver = "cosmo"
n_resample = 1000
significance_level = 0.05
p = [0.25, 0.0, 0.75]

# make data and get bandwidth
W = make_data(n_data, p)
h_ROT = estimate_ROT_bandwidth(W, "epanechnikov_order_2")

# fit dyadic kernel density estimator
est = DyadicKernelDensityEstimator(
    kernel_name, h_ROT, significance_level,
    n_resample, sdp_solver, evals, W, Dict())

fit(est)

# display properties of estimator
display(est)

# display evaluation points
display(evals')

# display point estimates
display(est.fhat')

# display pointwise confidence intervals
display(est.pci)

# display uniform confidence band
display(est.ucb)

Paper replication

Please refer to the replication README.