Estimation and variable selection of quantile partially linear additive models for correlated data

Abstract

AbstractLongitudinal data arise frequently in many economic studies and epidemiological research. In this paper, we investigate the partially linear additive model for longitudinal data in the framework of quantile regression. To incorporate the within-subject correlation, we develop an estimation procedure using quadratic inference function (QIF) and polynomial spline approximation for unknown nonparametric functions. The theoretical properties of the resulting estimators are established, where the nonparametric functions achieve the optimal convergence rate and the parametric components are asymptotically normal even when the number of parameters in the linear part is diverging. We also propose a variable selection procedure based on penalization. Since the objective function is discontinuous, a practical estimation procedure is proposed using induced smoothing and we prove that the smoothed estimator is asymptotically equivalent to the original estimator. The proposed methods are evaluated via simulation studies and a real data application.Keywords: Longitudinal datapartially linear additive modelsquadratic inference functionsquantile regressionAMS 2000 Subject Classifications: Primary 62G05Secondary 62G20 AcknowledgmentsWe sincerely thank the editors and reviewers for the comments that greatly improved the manuscript.Disclosure statementNo potential conflict of interest was reported by the author(s).