Asymptotic equivalence of empirical likelihood and Bayesian MAP

Details Asymptotic equivalence of empirical likelihood and Bayesian MAP Asymptotic equivalence of empirical likelihood and Bayesian MAP

2009-08-24

arxiv.org/abs/0908.3397v1

Annals of Statistics 2009, Vol. 37, No. 5A, 2445-2457

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-AOS645 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/08-AOS645

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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