2018/08/19 by Albert Vexler, Li Zou, Vexler, Albert +3
Mathematics · #Advanced Statistical Methods and Models #Applied mathematics #Asymptotically optimal algorithm #Bayesian probability #Density estimation #Empirical likelihood #Estimating equations #Estimation theory #FOS: Computer and information sciences #Kullback–Leibler divergence #Likelihood function #Marginal likelihood #Mathematical optimization #Mathematics #Maximum likelihood #Methodology (stat.ME) #Parametric statistics #Prior probability #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics #stat.ME
paper · pdf · doi:10.48550/arxiv.1808.06222
published in arXiv (Cornell University) (Cornell University)
arxiv created 2018/08/19 · openalex publication_date 2018/08/19 · arxiv updated 2018/08/21 · openalex created_date 2022/08/04 · openalex updated_date 2026/08/06
The practice of employing empirical likelihood (EL) components in place of\nparametric likelihood functions in the construction of Bayesian-type procedures\nhas been well-addressed in the modern statistical literature. We rigorously\nderive the EL prior, a Jeffreys-type prior, which asymptotically maximizes the\nShannon mutual information between data and the parameters of interest. The\nfocus of our approach is on an integrated Kullback-Leibler distance between the\nEL-based posterior and prior density functions. The EL prior density is the\ndensity function for which the corresponding posterior form is asymptotically\nnegligibly different from the EL. We show that the proposed result can be used\nto develop a methodology for reducing the asymptotic bias of solutions of\ngeneral estimating equations and M-estimation schemes by removing the\nfirst-order term. This technique is developed in a similar manner to methods\nemployed to reduce the asymptotic bias of maximum likelihood estimates via\npenalizing the underlying parametric likelihoods by their Jeffreys invariant\npriors. A real data example related to a study of myocardial infarction\nillustrates the attractiveness of the proposed technique in practical aspects.\n Keywords: Asymptotic bias, Biased estimating equations, Empirical likelihood,\nExpected Kullback-Leibler distance, Penalized likelihood, Reference prior.\n