Feature screening in ultrahigh-dimensional partially linear models with missing responses at random

Abstract

This paper proposes a new feature screening procedure in ultrahigh-dimensional partially linear models with missing responses at random for longitudinal data based on the profile marginal kernel-assisted estimating equations imputation technique. The proposed feature screening procedure has three key merits. First, it is computationally efficient, and can be used to screen significant covariates in the presence of missing responses. Second, it does not require estimating respondent probability and is robust to the misspecification of respondent probability models. Third, the univariate kernel smoothing method is adopted to estimate nonparametric functions, and is employed to impute estimating equations with missing responses at random, which avoids the well-known “curse of dimensionality”. The ranking consistency property and the sure screening property are shown under some regularity conditions. Simulation studies are conducted to investigate the finite sample performance of the proposed screening procedure. An example is used to illustrate the proposed procedure.