Bayesian Variable Selection and Estimation Based on Global-Local Shrinkage Priors

Xueying Tang, Xiaofan Xu, Malay Ghosh, Prasenjit Ghosh

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We consider in this paper simultaneous Bayesian variable selection and estimation for linear regression models with global-local shrinkage priors on the regression coefficients. We propose a variable selection procedure that selects a variable if the ratio of the posterior mean of its regression coefficient to the corresponding ordinary least square estimate is greater than a half. The regression coefficient is estimated by the posterior mean or zero depending on whether the corresponding variable is selected or not. Under the assumption of orthogonal designs, we prove that if the local parameters have polynomial-tailed priors, the proposed method enjoys the oracle property in the sense that it can achieve variable selection consistency and optimal estimation rate at the same time. However, if, instead, an exponential-tailed prior is used for the local parameters, the proposed method has variable selection consistency but not the optimal estimation rate. We show via simulation and real data examples that our proposed selection mechanism works for nonorthogonal designs as well.

Original languageEnglish (US)
Pages (from-to)215-246
Number of pages32
JournalSankhya A
Volume80
Issue number2
DOIs
StatePublished - Aug 1 2018
Externally publishedYes

Keywords

  • 62J05; Secondary 62J07
  • Half-thresholding
  • Optimal estimation rate
  • Primary 62F15
  • Variable selection consistency

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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