An Adaptive Resampling Test for Detecting the Presence of Significant Predictors
针对高维回归中变量筛选后估计量极限行为非标准的问题，提出自适应重抽样检验，为控制族系错误率提供Bonferroni方法的替代方案，并在模拟和基因表达、HIV耐药数据中验证效果。
This paper 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 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 gene expression data and HIV drug resistance data.