Variable Selection via Partial Correlation

• Activity Number: 498 - Statistica Sinica Invited Papers Session
• Type: Invited
• Date/Time: Wednesday, August 1, 2018 : 10:30 AM to 12:20 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Runze Li* and Jingyuan Liu and Lejie Lou
• Companies: Penn State University and Xiamen University and Ernst & Young
• Keywords: Elliptical distribution; model selection consistency; partial correlation; partial faithfulness; sure screening property; ultrahigh dimensional linear model

Abstract

This paper addresses two important issues related to partial correlation based variable selection method (Buhlmann, et al, 2010): (a) whether this method is sensitive to normality assumption, and (b) whether this method is valid when the dimension of predictor increases in an exponential rate of the sample size. To address issue (a), we systematically study this method for elliptical linear regression models. Our finding indicates that the original proposal may lead to inferior performance when the marginal kurtosis of predictor is not close to that of normal distribution. Our simulation results further confirm this finding. To ensure the superior performance of partial correlation based variable selection procedure, we propose a thresholded partial correlation (TPC) approach to select significant variables in linear regression models. We establish the selection consistency of the TPC in the presence of ultrahigh dimensional predictors. Since the TPC procedure includes the original proposal as a special case, our theoretical results address the issue (b) directly. As a by-product, the sure screening property of the first step of TPC was obtained.