The Annals of Statistics

Quantile regression in partially linear varying coefficient models

Huixia Judy Wang, Zhongyi Zhu, and Jianhui Zhou

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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.

Article information

Ann. Statist., Volume 37, Number 6B (2009), 3841-3866.

First available in Project Euclid: 23 October 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression
Secondary: 62G10: Hypothesis testing

Basis spline longitudinal data marginal model rank score test semiparametric


Wang, Huixia Judy; Zhu, Zhongyi; Zhou, Jianhui. Quantile regression in partially linear varying coefficient models. Ann. Statist. 37 (2009), no. 6B, 3841--3866. doi:10.1214/09-AOS695.

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