Stepwise Regression Method for High-Dimensional Variable Selection

• Activity Number: 577
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Jing-Shiang Hwang*+ and Tsuey-Hwa Hu
• Companies: Academia Sinica and Academia Sinica
• Keywords: Stepwise regression ; Forward regression ; Variable selection ; High-dimensional data

Abstract

Stepwise regression is a very popular and classical variable screening method which has been widely accepted by practical analysts. Wang (JASA, 2009) showed that forward regression with an extended Bayesian information criterion can identify theoretically all relevant predictors consistently under an ultrahigh-dimensional setup and some assumptions. Ing and Lai (Stat Sinica, 2011) further introduced a fast stepwise regression method which has oracle property under a strong sparsity assumption. Both methods showed very impressive performances in each own simulation scenarios respectively. However, each method performed badly under the other's simulation scheme. It indicates that these two novel stepwise methods may be too sensitive to their own assumptions. This study is motivated to develop a more robust stepwise method for screening high-dimensional data. The idea is to establish a new stopping rule other than the conventional information criteria for lessening model assumptions. We demonstrate satisfactory performance of the proposed method in the comparisons with the two stepwise regression methods using the same simulation setups in these two papers.