Bayesian exponentially tilted empirical likelihood

• 成果类型: Article
• 署名作者: Schennach, SM
• 署名单位: University of Chicago
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/92.1.31
• 发表日期: 2005
• 页码: 3146
• 关键词: ratio confidence-intervals; generalized-method; MOMENTS ESTIMATION; sample properties; MAXIMUM-ENTROPY; estimators; inference; models; distributions; bootstrap

摘要

While empirical likelihood has been shown to exhibit many of the properties of conventional parametric likelihoods, a formal probabilistic interpretation has so far been lacking. We show that a likelihood function very closely related to empirical likelihood naturally arises from a nonparametric Bayesian procedure which places a type of noninformative prior on the space of distributions. This prior gives preference to distributions having a small support and, among those sharing the same support, it favours entropy-maximising distributions. The resulting nonparametric Bayesian procedure admits a computationally convenient representation as an empirical-likelihood-type likelihood where the probability weights are obtained via exponential tilting. The proposed methodology provides an attractive alternative to the Bayesian bootstrap as a nonparametric limit of a Bayesian procedure for moment condition models.