Miscellanea. Probability matching priors for non-regular cases

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Abstract
We study probability matching priors in non-regular cases. Both one-parameter and multi-parameter cases are considered. The resulting priors are shown to satisfy certain differential equations. Several examples are discussed. It is observed that the reference prior in the sense of Bernardo is in many cases also probability matching. As a necessary tool for finding such priors, asymptotic expansion of posterior distributions for multi-parameter non-regular cases is also obtained.

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