Grouped variable screening for ultra-high dimensional data for linear model

Abstract

Ultra-high dimensional data sets often need a screening step that removes irrelevant variables prior to the main analysis. In high-dimensional linear regression, screening relevant predictors before the model estimation often yields a better prediction accuracy and much faster computation. However, most existing screening approaches target on individual predictors, thus are not able to incorporate structured predictors, such as dummy variables and grouped variables. New screening methods for naturally grouped predictors for high dimensional linear regression are presented. Two popular variable screening methods are generalized to the grouped predictors case, and also a novel screening procedure is proposed. Asymptotic sure screening properties for all three methods are established. Also empirical benefits of the screening approaches via simulation and a real data analysis are demonstrated. Specifically, a two-step analysis that does a screening followed by a sparse estimation improves the prediction accuracy as well as computing time, compared to one-stage sparse regression.