Bernoulli

  • Bernoulli
  • Volume 23, Number 3 (2017), 1822-1847.

Empirical Bayes posterior concentration in sparse high-dimensional linear models

Ryan Martin, Raymond Mess, and Stephen G. Walker

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Abstract

We propose a new empirical Bayes approach for inference in the $p\gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a variety of concentration rate results for the empirical Bayes posterior distribution, relevant for both estimation and model selection. Computation is straightforward and fast, and simulation results demonstrate the strong finite-sample performance of the empirical Bayes model selection procedure.

Article information

Source
Bernoulli, Volume 23, Number 3 (2017), 1822-1847.

Dates
Received: September 2015
Revised: December 2015
First available in Project Euclid: 17 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1489737626

Digital Object Identifier
doi:10.3150/15-BEJ797

Mathematical Reviews number (MathSciNet)
MR3624879

Zentralblatt MATH identifier
06714320

Keywords
data-dependent prior fractional likelihood minimax regression variable selection

Citation

Martin, Ryan; Mess, Raymond; Walker, Stephen G. Empirical Bayes posterior concentration in sparse high-dimensional linear models. Bernoulli 23 (2017), no. 3, 1822--1847. doi:10.3150/15-BEJ797. https://projecteuclid.org/euclid.bj/1489737626


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