Varying-coefficient quantile regression with effect under panel data and missing observation

Abstract

We, in this paper, focus on partial linear varying-coefficient quantile regression with fixed effects under panel data and missing observations, where the missing observations include either responses or covariates are missing at random. Under independent setting, we define estimators of the unknown parameter vector, varying-coefficient function and effect in the model, and discuss their large number properties. To use the information from within-subject correlations, we propose weighted estimators for the unknown amounts, where the weights are chosen based on mean and quantile regressions, respectively, by quadratic inference technique and empirical likelihood method. Under dependent assumption, we establish asymptotic normality of the weighted estimators. Meanwhile, we study hypothesis tests of the parameter, varying-coefficient function and effect, and prove asymptotic distributions of restricted estimators and test statistics of the parameter under null hypothesis and local alternative hypothesis, respectively. Also, oracle property of the parameter is considered. Simulation study and real data analysis are conducted to evaluate the performance of the proposed methods.