Asymptotic Normality of M-Estimators for Varying Coefficient Models with Longitudinal Data

Abstract

This article considers a nonparametric varying coefficient regression model with longitudinal observations. The relationship between the dependent variable and the covariates is assumed to be linear at a specific time point, but the coefficients are allowed to change over time. A general formulation is used to treat mean regression, median regression, quantile regression, and robust mean regression in one setting. The local M-estimators of the unknown coefficient functions are obtained by local linear method. The asymptotic distributions of M-estimators of unknown coefficient functions at both interior and boundary points are established. Various applications of the main results, including estimating conditional quantile coefficient functions and robustifying the mean regression coefficient functions are derived. Finite sample properties of our procedures are studied through Monte Carlo simulations.

Keywords:

• Asymptotic normality
• Longitudinal data
• M-estimator
• Quantile regression
• Robust smoother
• Varying coefficient model

Mathematics Subject Classification:

• Primary 62G05, 62G35
• Secondary 62G08, 62G20

Acknowledgments

This research is partially supported by National Natural Science Foundation of China (Grant No. 10671089), China Postdoctoral Science Foundation funded project, and Jiangsu Planned Projects for Postdoctoral Research Fund.