WEAK SIGNAL IDENTIFICATION AND INFERENCE IN PENALIZED MODEL SELECTION

• 成果类型: Article
• 署名作者: Shi, Peibei; Qu, Annie
• 署名单位: University of Michigan System; University of Michigan; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1482
• 发表日期: 2017
• 页码: 1214-1253
• 关键词: MAXIMUM-LIKELIHOOD ESTIMATORS; adaptive lasso; confidence-intervals; variable selection; parameter

摘要

Weak signal identification and inference are very important in the area of penalized model selection, yet they are underdeveloped and not well studied. Existing inference procedures for penalized estimators are mainly focused on strong signals. In this paper, we propose an identification procedure for weak signals in finite samples, and provide a transition phase in-between noise and strong signal strengths. We also introduce a new two-step inferential method to construct better confidence intervals for the identified weak signals. Our theory development assumes that variables are orthogonally designed. Both theory and numerical studies indicate that the proposed method leads to better confidence coverage for weak signals, compared with those using asymptotic inference. In addition, the proposed method outperforms the perturbation and bootstrap resampling approaches. We illustrate our method for HIV antiretroviral drug susceptibility data to identify genetic mutations associated with HIV drug resistance.