Empirical-type likelihoods allowing posterior credible sets with frequentist validity: Higher-order asymptotics

• 成果类型: Article
• 署名作者: Fang, Kai-Tai; Mukerjee, Rahul
• 署名单位: Hong Kong Baptist University; Indian Institute of Management (IIM System); Indian Institute of Management Calcutta
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/93.3.723
• 发表日期: 2006
• 页码: 723733
• 关键词: probability matching priors; discrepancy statistics; confidence-intervals; bartlett correction

摘要

With reference to a general class of empirical-type likelihoods, we develop higher-order asymptotics for the frequentist coverage of Bayesian credible sets based on posterior quantiles and highest posterior density. These asymptotics, in turn, characterise members of the class that allow approximate frequentist validity of such sets. It is seen that the usual empirical likelihood does not enjoy this property up to the order of approximation considered here.