An Adaptive Resampling Test for Detecting the Presence of Significant Predictors

Abstract

This article investigates 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 nonstandard 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 family-wise 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 nonstandard asymptotics in the tightest way possible. The performance of the approach is evaluated using a simulation study and applied to gene expression data and HIV drug resistance data.

• Bootstrap
• Family-wise error rate
• Marginal regression
• Nonregular asymptotics
• Screening covariates

Additional information

Notes on contributors

Ian W. McKeague

Ian W. McKeague (E-mail: [email protected]) is Professor, and Min Qian (E-mail: [email protected]) is Assistant Professor, Department of Biostatistics, Columbia University, New York, NY 10027. Research of the first author is supported by NIH Grant R01GM095722-01 and NSF Grant DMS-1307838. Research of the second author is supported by NSF Grant DMS-1307838.

Min Qian

Ian W. McKeague (E-mail: [email protected]) is Professor, and Min Qian (E-mail: [email protected]) is Assistant Professor, Department of Biostatistics, Columbia University, New York, NY 10027. Research of the first author is supported by NIH Grant R01GM095722-01 and NSF Grant DMS-1307838. Research of the second author is supported by NSF Grant DMS-1307838.