Robust Estimation and Variable Selection for Partially Linear Additive Model Under Missing Data

Abstract

In this paper, we investigate the robust estimation and variable selection for partially linear additive model under response missing at random. The nonparametric functions are approximated by B-spline basis. The variable selection of parametric and nonparametric components simultaneously are realized by combining modal regression method and double-SCAD penalty function. We can prove that the variable selection method has Oracle property under some regularity conditions. Some simulation studies are carried out to assess the performance of the proposed methods.