Data-dependent probability matching priors for highest posterior density and equal-tailed two-sided regions based on empirical-type likelihoods |
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Authors: | In Hong Chang Rahul Mukerjee |
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Institution: | 1. Department of Computer Science and Statistics, Chosun University, Gwangju 501-759, South Korea;2. Indian Institute of Management Calcutta, Joka, Diamond Harbour Road, Kolkata 700 104, India |
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Abstract: | We consider a very general class of empirical-type likelihoods which includes the usual empirical likelihood and all its major variants proposed in the literature. It is known that none of these likelihoods admits a data-free probability matching prior for the highest posterior density region. We develop necessary higher order asymptotics to show that at least for the usual empirical likelihood this difficulty can be resolved if data-dependent priors are entertained. A related problem concerning the equal-tailed two-sided posterior credible region is also investigated. A simulation study is seen to lend support to the theoretical results. |
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Keywords: | 62F25 |
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