Nonparametric independence screening for ultra-high dimensional generalized varying coefficient models with longitudinal data

Abstract

In this paper, we propose a nonparametric independence screening method for sparse ultra-high dimensional generalized varying coefficient models with longitudinal data. Our methods combine the ideas of sure independence screening (SIS) in sparse ultra-high dimensional generalized linear models and varying coefficient models with the marginal generalized estimating equation (GEE) method, called NIS-GEE, considering both the marginal correlation between response and covariates, and the subject correlation for variable screening. The corresponding iterative algorithm is introduced to enhance the performance of the proposed NIS-GEE method. Furthermore it is shown that, under some regularity conditions, the proposed NIS-GEE method enjoys the sure screening properties. Simulation studies and a real data analysis are used to assess the performance of the proposed method.