Local nonparametric quantile regression

This Julia package implements the nonparametric quantile regression approach of Ye and Padilla (2020).

Usage

The following example simulates heteroscedastic data and estimates the 20th, 50th,and 80th conditional quantiles.

using QuantileNN, Plots, StableRNGs, LaTeXStrings, Statistics, Printf, Distributions
rng = StableRNG(123)

n = 1000
p = 3
X = randn(rng, n, p)
X[:, 1] .= 1
y = X[:, 2] + (1 .+ 2*abs.(X[:, 2])) .* randn(n)

pp = [0.2, 0.5, 0.8]
mm = [fit(QNN, X, y; p=p) for p in pp]

x = range(-2, 2, 20)
bw = 1.0
yy = [[predict_smooth(m, [0, v, 0], [bw]) for v in x] for m in mm]

ps = [@sprintf("%.2f", p) for p in pp]
plt = plot(x, yy[1], label=ps[1], xlabel=L"$x$", ylabel=L"$y$", size=(400,300))
plt = plot!(plt, x, yy[2], label=ps[2])
plt = plot!(plt, x, yy[3], label=ps[3])
Plots.savefig(plt, "./assets/readme1.svg")

Example plot 1

References

[1] Steven Siwei Ye and Oscar Hernan Madrid Padilla. Non-parametric Quantile Regression via the K-NN Fused Lasso. https://arxiv.org/abs/2012.01758

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