Quantile regression with varying coefficients

TL;DR

This paper introduces a flexible nonparametric quantile regression method with varying coefficients using polynomial splines, including estimation, testing, and empirical validation on health data.

Contribution

It develops a novel spline-based approach for nonparametric quantile regression with varying coefficients, along with a Rao-score test and asymptotic analysis.

Findings

Estimators are computationally straightforward using standard algorithms.

The Rao-score test effectively assesses model linearity.

Empirical application demonstrates practical utility.

Abstract

Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider conditional quantiles with varying coefficients and propose a methodology for their estimation and assessment using polynomial splines. The proposed estimators are easy to compute via standard quantile regression algorithms and a stepwise knot selection algorithm. The proposed Rao-score-type test that assesses the model against a linear model is also easy to implement. We provide asymptotic results on the convergence of the estimators and the null distribution of the test statistic. Empirical results are also provided, including an application of the methodology to forced expiratory volume (FEV) data.