The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. The EL prior, a Jeffreys-type prior, which asymptotically maximizes the Shannon mutual information between data and the parameters of interest, is rigorously derived. The focus of the proposed approach is on an integrated Kullback-Leibler distance between the EL-based posterior and prior density functions. The EL prior density is the density function for which the corresponding posterior form is asymptotically negligibly different from the EL. The proposed result can be used to develop a methodology for reducing the asymptotic bias of solutions of general estimating equations and M-estimation schemes by removing the first-order term. This technique is developed in a similar manner to methods employed to reduce the asymptotic bias of maximum likelihood estimates via penalizing the underlying parametric likelihoods by their Jeffreys invariant priors. A real data example related to a study of myocardial infarction illustrates the attractiveness of the proposed technique in practical aspects.

中文翻译：

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应用于一般估计方程偏差减少的经验似然先验

在贝叶斯类型程序的构建中使用经验似然 (EL) 组件代替参数似然函数的做法在现代统计文献中得到了很好的解决。EL 先验是一种 Jeffreys 类型的先验，它渐近最大化数据和感兴趣参数之间的香农互信息，是严格推导出来的。所提出方法的重点是基于 EL 的后验和先验密度函数之间的综合 Kullback-Leibler 距离。EL 先验密度是对应的后验形式与 EL 渐近可忽略不计的密度函数。所提出的结果可用于开发一种通过去除一阶项来减少一般估计方程和 M 估计方案的解的渐近偏差的方法。该技术的开发方式与用于减少最大似然估计的渐近偏差的方法类似，通过它们的 Jeffreys 不变先验来惩罚潜在的参数似然。一个与心肌梗塞研究相关的真实数据示例说明了所提出的技术在实际方面的吸引力。