Open Access
June 2017 Weak signal identification and inference in penalized model selection
Peibei Shi, Annie Qu
Ann. Statist. 45(3): 1214-1253 (June 2017). DOI: 10.1214/16-AOS1482


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.


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Peibei Shi. Annie Qu. "Weak signal identification and inference in penalized model selection." Ann. Statist. 45 (3) 1214 - 1253, June 2017.


Received: 1 May 2015; Revised: 1 February 2016; Published: June 2017
First available in Project Euclid: 13 June 2017

zbMATH: 1371.62025
MathSciNet: MR3662453
Digital Object Identifier: 10.1214/16-AOS1482

Primary: 62F30 , 62J07
Secondary: 62E15

Keywords: Adaptive LASSO , finite sample inference , Model selection , weak signal

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 3 • June 2017
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