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

Xueying Tang (), Xiaofan Xu, Malay Ghosh and Prasenjit Ghosh
Additional contact information
Xueying Tang: University of Florida
Xiaofan Xu: Stubhub Inc.
Malay Ghosh: University of Florida
Prasenjit Ghosh: Presidency University

Sankhya A: The Indian Journal of Statistics, 2018, vol. 80, issue 2, No 2, 215-246

Abstract: 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.

Keywords: Half-thresholding; Optimal estimation rate; Variable selection consistency.; Primary 62F15, 62J05; Secondary 62J07 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s13171-017-0118-2

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