Journal
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE
Volume 32, Issue 2, Pages 119-137Publisher
WILEY
DOI: 10.2307/3315937
Keywords
partial information; local limit theorem; posterior normality
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The authors establish the asymptotic normality and determine the limiting variance of the posterior density for a multivariate parameter, given the value of a consistent and asymptotically Gaussian statistic satisfying a uniform local central limit theorem. Their proof is given in the continuous case but generalizes to lattice-valued random variables. It hinges on a uniform Edgeworth expansion used to control the behaviour of the conditioning statistic. They provide examples and show bow their result can help in identifying reference priors.
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