Quantile regression in partially linear varying coefficient models

TL;DR

This paper introduces a flexible semiparametric quantile regression method for longitudinal data with varying coefficients, providing easy implementation, asymptotic theory, and hypothesis testing without error distribution assumptions.

Contribution

It develops a novel estimation and testing framework for partially linear quantile models with varying coefficients, including rank score tests and basis function approximation techniques.

Findings

Method performs well in finite samples as shown by simulations.

Application to AIDS data demonstrates richer insights than traditional methods.

Asymptotic properties are established for both constant and varying coefficients.

Abstract

Semiparametric models are often considered for analyzing longitudinal data for a good balance between flexibility and parsimony. In this paper, we study a class of marginal partially linear quantile models with possibly varying coefficients. The functional coefficients are estimated by basis function approximations. The estimation procedure is easy to implement, and it requires no specification of the error distributions. The asymptotic properties of the proposed estimators are established for the varying coefficients as well as for the constant coefficients. We develop rank score tests for hypotheses on the coefficients, including the hypotheses on the constancy of a subset of the varying coefficients. Hypothesis testing of this type is theoretically challenging, as the dimensions of the parameter spaces under both the null and the alternative hypotheses are growing with the sample size. We assess the finite sample performance of the proposed method by Monte Carlo simulation studies, and demonstrate its value by the analysis of an AIDS data set, where the modeling of quantiles provides more comprehensive information than the usual least squares approach.