Efficient estimation in the partially linear quantile regression model for longitudinal data

The focus of this study is efficient estimation in a quantile regression model with partially linear coefficients for longitudinal data, where repeated measurements within each subject are likely to be correlated. We propose a weighted quantile regression approach for time-invariant and time-varying coefficient estimation. The proposed approach can employ two types of weights obtained from an empirical likelihood method to account for the within-subject correlation: the global weight using all observations and the local weight using observations in the neighborhood of the time point of interest. We investigate the influence of choice of weights on asymptotic estimation efficiency and find theoretical results that are counter intuitive; it is essential to use the global weight for both time-invariant and time-varying coefficient estimation. This benefits from the within-subject correlation and prevents an adverse effect due to the weight discordance. For statistical inference, a random perturbation approach is utilized and evaluated through simulation studies. The proposed approach is also illustrated through a Multi-Center AIDS Cohort study.