Quantile regression of partially linear single-index model with missing observations

Abstract

In this paper, we discuss the quantile regression and variable selection of partially linear single-index model when data are missing at random, which allows the response and covariates missing simultaneously. By using iteration algorithm and local linear method, we construct the inverse probability weighted quantile estimators of both the parameters and the link function. The penalized estimator of the parameters is also considered based on the adaptive LASSO penalty. The asymptotic distributions and the oracle property of the proposed estimators are derived. Simulation study and real data analysis are presented to show the performance of the proposed methods.