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April 2017 Asymptotic behaviour of the empirical Bayes posteriors associated to maximum marginal likelihood estimator
Judith Rousseau, Botond Szabo
Ann. Statist. 45(2): 833-865 (April 2017). DOI: 10.1214/16-AOS1469

Abstract

We consider the asymptotic behaviour of the marginal maximum likelihood empirical Bayes posterior distribution in general setting. First, we characterize the set where the maximum marginal likelihood estimator is located with high probability. Then we provide oracle type of upper and lower bounds for the contraction rates of the empirical Bayes posterior. We also show that the hierarchical Bayes posterior achieves the same contraction rate as the maximum marginal likelihood empirical Bayes posterior. We demonstrate the applicability of our general results for various models and prior distributions by deriving upper and lower bounds for the contraction rates of the corresponding empirical and hierarchical Bayes posterior distributions.

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Judith Rousseau. Botond Szabo. "Asymptotic behaviour of the empirical Bayes posteriors associated to maximum marginal likelihood estimator." Ann. Statist. 45 (2) 833 - 865, April 2017. https://doi.org/10.1214/16-AOS1469

Information

Received: 1 April 2015; Revised: 1 March 2016; Published: April 2017
First available in Project Euclid: 16 May 2017

zbMATH: 1371.62048
MathSciNet: MR3650402
Digital Object Identifier: 10.1214/16-AOS1469

Subjects:
Primary: 60K35 , 62G05 , 62G20
Secondary: 62G07 , 62G08

Keywords: Adaptation , Density estimation , Empirical Bayes , Gaussian prior , hierarchical Bayes , Nonparametric regression , Posterior contraction rates , truncation prior

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 2 • April 2017
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