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October 2009 Asymptotic equivalence of empirical likelihood and Bayesian MAP
Marian Grendár, George Judge
Ann. Statist. 37(5A): 2445-2457 (October 2009). DOI: 10.1214/08-AOS645

Abstract

In this paper we are interested in empirical likelihood (EL) as a method of estimation, and we address the following two problems: (1) selecting among various empirical discrepancies in an EL framework and (2) demonstrating that EL has a well-defined probabilistic interpretation that would justify its use in a Bayesian context. Using the large deviations approach, a Bayesian law of large numbers is developed that implies that EL and the Bayesian maximum a posteriori probability (MAP) estimators are consistent under misspecification and that EL can be viewed as an asymptotic form of MAP. Estimators based on other empirical discrepancies are, in general, inconsistent under misspecification.

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Marian Grendár. George Judge. "Asymptotic equivalence of empirical likelihood and Bayesian MAP." Ann. Statist. 37 (5A) 2445 - 2457, October 2009. https://doi.org/10.1214/08-AOS645

Information

Published: October 2009
First available in Project Euclid: 15 July 2009

zbMATH: 1173.62014
MathSciNet: MR2543698
Digital Object Identifier: 10.1214/08-AOS645

Subjects:
Primary: 62C10, 62G05
Secondary: 60F10

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 5A • October 2009
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