Hypothesis testing sure independence screening for nonparametric regression

Abstract

In this paper we develop a sure independence screening method based on hypothesis testing (HT-SIS) in a general nonparametric regression model. The ranking utility is based on a powerful test statistic for the hypothesis of predictive significance of each available covariate. The sure screening property of HT-SIS is established, demonstrating that all active predictors will be retained with high probability as the sample size increases. The threshold parameter is chosen in a theoretically justified manner based on the desired false positive selection rate. Simulation results suggest that the proposed method performs competitively against procedures found in the literature of screening for several models, and outperforms them in some scenarios. A real dataset of microarray gene expressions is analyzed.