An Adaptive Resampling Test for Detecting the Presence of Significant Predictors

• Activity Number: 407
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Ian Wray McKeague and Min Qian*+
• Companies: Columbia University and Columbia University
• Keywords: Bootstrap ; Family-wise error rate ; Marginal regression ; Screening covariates

Abstract

This paper constructs a screening procedure based on marginal regression to detect the presence of a significant predictor. Standard inferential methods are known to fail in this setting due to the nonregular limiting behavior of the estimated regression coefficient of the selected predictor; in particular, the limiting distribution is discontinuous at zero as a function of the regression coefficient of the predictor maximally correlated with the outcome. To circumvent this nonregularity, we propose a bootstrap procedure based a local model in order to better reflect small-sample behavior at a root-n scale in the neighborhood of zero. The proposed test is adaptive in the sense that it employs thresholding to distinguish situations in which a centered percentile bootstrap applies, and otherwise adapts to the local asymptotic behavior of the test statistic in a way that depends continuously on the local parameter. The performance of the approach is evaluated using a simulation study, and applied to an example involving gene expression data.