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August 2017 Empirical Bayes posterior concentration in sparse high-dimensional linear models
Ryan Martin, Raymond Mess, Stephen G. Walker
Bernoulli 23(3): 1822-1847 (August 2017). DOI: 10.3150/15-BEJ797


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.


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Ryan Martin. Raymond Mess. Stephen G. Walker. "Empirical Bayes posterior concentration in sparse high-dimensional linear models." Bernoulli 23 (3) 1822 - 1847, August 2017.


Received: 1 September 2015; Revised: 1 December 2015; Published: August 2017
First available in Project Euclid: 17 March 2017

zbMATH: 06714320
MathSciNet: MR3624879
Digital Object Identifier: 10.3150/15-BEJ797

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability


Vol.23 • No. 3 • August 2017
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