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Asymptotic normality of the posterior given a statistic
Author(s) -
Yuan Ao,
Clarke Bertrand
Publication year - 2004
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315937
Subject(s) - mathematics , asymptotic distribution , statistic , central limit theorem , gaussian , statistics , multivariate normal distribution , normality , prior probability , local asymptotic normality , ancillary statistic , multivariate statistics , test statistic , estimator , statistical hypothesis testing , bayesian probability , physics , quantum mechanics
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 how their result can help in identifying reference priors.