Nonparametric independence screening for ultra-high-dimensional longitudinal data under additive models

Abstract

ABSTRACTUltra-high-dimensional data are frequently seen in many contemporary statistical studies, which pose challenges both theoretically and methodologically. To address this issue under longitudinal data setting, we propose a marginal nonparametric screening method to hunt for the relevant covariates in additive models. A new data-driven thresholding and an iterative procedure are developed. Especially, a sample splitting method is proposed to further reduce the false selection rates. Although the repeated measurements within each subjects are correlated, the sure screening property is theoretically established. To the best of our knowledge, screening for longitudinal data rarely appeared in the literatures, and our method can be regarded as a nontrivial extension of nonparametric independence screening method. An extensive simulation study is conducted to illustrate the finite sample performance of the proposed method and procedure. Finally, the proposed method is applied to a yeast cycle gene expression data set to identify cell cycle-regulated genes and transcription factors.