Weak signal identification and inference in penalized model selection

Peibei Shi, Annie Qu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1214-1253
Number of pages40
JournalAnnals of Statistics
Issue number3
StatePublished - Jun 2017


  • Adaptive Lasso
  • Finite sample inference
  • Model selection
  • Weak signal

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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