Group screening for ultra-high-dimensional feature under linear model

Abstract

Ultra-high-dimensional data with grouping structures arise naturally in many contemporary statistical problems, such as gene-wide association studies and the multi-factor analysis-of-variance (ANOVA). To address this issue, we proposed a group screening method to do variables selection on groups of variables in linear models. This group screening method is based on a working independence, and sure screening property is also established for our approach. To enhance the finite sample performance, a data-driven thresholding and a two-stage iterative procedure are developed. To the best of our knowledge, screening for grouped variables rarely appeared in the literature, and this method can be regarded as an important and non-trivial extension of screening for individual variables. An extensive simulation study and a real data analysis demonstrate its finite sample performance.