ASYMPTOTIC EQUIVALENCE OF EMPIRICAL LIKELIHOOD AND BAYESIAN MAP

• 成果类型: Article
• 署名作者: Grendar, Marian; Judge, George
• 署名单位: Matej Bel University; Slovak Academy of Sciences; Institute of Measurement Science, SAS; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS645
• 发表日期: 2009
• 页码: 2445-2457
• 关键词: inference

摘要

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 mis-specification and that EL can be viewed as an asymptotic form of MAP. Estimators based on other empirical discrepancies are, in general. inconsistent under misspecification.