The Annals of Statistics
- Ann. Statist.
- Volume 37, Number 5A (2009), 2445-2457.
Asymptotic equivalence of empirical likelihood and Bayesian MAP
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.
Ann. Statist. Volume 37, Number 5A (2009), 2445-2457.
First available in Project Euclid: 15 July 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G05: Estimation 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 60F10: Large deviations
Grendár, Marian; Judge, George. Asymptotic equivalence of empirical likelihood and Bayesian MAP. Ann. Statist. 37 (2009), no. 5A, 2445--2457. doi:10.1214/08-AOS645. https://projecteuclid.org/euclid.aos/1247663761.