Longitudinal Data Of Components In A Partly Linear Model Under Quantile Regression

The partially linear model is an important semiparametric statistical model. Longitudinal data are referred to data in which the same sample or individual is measured repeatedly through time or space. The prominent advantage of longitudinal data is that it can analyze effectively the change of individuals over time and variation among individuals. However, quantile regression models the relationship between covariate and the given conditional quantiles.In this paper, we study the estimations in the partially linear model for longitudinal data. The main contents are as follows:(1) Based on the quantile regression methods and the usual nonparametric weight function method, we construct the estimators of the parametric and nonparametric components. The asymptotic normality of the parametric estimator and the optimal convergence rate of the nonparametric estimator are also obtained under the suitable conditions.(2) Based on the empirical likelihood method and the smooth empirical likelihood (SEL) approach, we get the maximum EL and SEL estimators of the parametric component, respectively. Under some regularity conditions, it is proved that the maximum EL estimators and the SEL estimators have the same asymptotic distribution as the standard quantile regression estimator.