Weak Signal Identification and Inference in Penalized Model Selection

TL;DR

This paper introduces a novel approach for identifying and making inferences about weak signals in penalized model selection, providing more accurate confidence intervals and outperforming existing methods.

Contribution

It proposes a finite-sample weak signal identification procedure and a two-step inference method that improves confidence interval accuracy for weak signals under orthogonal design.

Findings

Better confidence coverage for weak signals compared to asymptotic inference.

Outperforms perturbation and bootstrap resampling methods.

Effective application demonstrated on HIV drug resistance data.

Abstract

Weak signal identification and inference are very important in the area of penalized model selection, yet they are under-developed 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 pro- vide 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 out- performs 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.