An Adaptive Resampling Test for Detecting the Presence of Significant Predictors

• Activity Number: 159
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: JASA, Theory and Methods
• Author(s): Ian McKeague*
• Companies: Columbia University
• Keywords: predictor screening ; high-dimensional regression ; oracle property ; resampling test ; multiple testing ; bootstrap

Abstract

This talk discusses marginal screening for detecting the presence of significant predictors in high-dimensional regression. Screening large numbers of predictors is a challenging problem due to the non-standard limiting behavior of post-model-selected estimators. There is a common misconception that the oracle property for such estimators is a panacea, but the oracle property only holds away from the null hypothesis of interest in marginal screening. To address this difficulty, we propose an adaptive resampling test (ART). Our approach provides an alternative to the popular (yet conservative) Bonferroni method of controlling familywise error rates. ART is adaptive in the sense that thresholding is used to decide whether the centered percentile bootstrap applies, and otherwise adapts to the non-standard asymptotics in the tightest way possible. The performance of the approach is evaluated using a simulation study, and applied to an example involving gene expression data.