Weak Signal's Identification and Inference in Penalized Model Selection

• Activity Number: 126
• Type: Topic Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Peibei Shi* and Annie Qu
• Companies: University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
• Keywords: model selection ; weak signal ; finite sample inference ; adaptive LASSO

Abstract

Penalized model selection methods are developed to select variables and estimate coefficients simultaneously, which is useful in high-dimensional variable selection. However, identification and inference for weak signals are still quite challenging and are not well-studied. Existing inference procedures for the penalized estimators are mainly focused on strong signals. This motivates us to investigate finite sample behavior for weak signal inference. We propose an identification procedure for weak signals in finite samples, and provide a transition phase in-between noise and strong signal strengths. A new two-step inferential method is introduced to construct better inference for the weak signals being identified. Our simulation studies show that the proposed method leads to better confidence coverages for weak signals, compared with those using asymptotic inference, perturbation and bootstrap resampling approaches. We also illustrate our method for HIV antiretroviral drug susceptibility data to identify genetic mutations associated with HIV drug resistance.