Asymptotic bayesian inference in some nonstandard cases: Bernstein–von Mises Results and regular bayes' estimators
作者:
R.C. Phoha,
期刊:
Statistics
(Taylor Available online 1987)
卷期:
Volume 18,
issue 2
页码: 259-274
ISSN:0233-1888
年代: 1987
DOI:10.1080/02331888708802016
出版商: Akademie-Verlag
关键词: Primary 62A15;secondary 62E20;asymptotic normality of posterior distributions;BERNSTEIN–VON MISES theorem;maximum likelihood estimates;multivariate statistical analysis;nonstandard cases;regular BAYES' estimators;regular loss funtions
数据来源: Taylor
摘要:
Asymptotically with probability close to one, the convergence in variation (also in distribution) to the multivariate normal, of the aposteriori density function of a parameter agains an apriori density, viz. the BERNSTEIN–VON MISES results are established when observations are not necessarily indenpendent or identically distributed but satisfy weak regularity assumptions on their joint density function. Regular BAYES' estimators are defined with respect to regular loss functions and a positive apriori density and proved consistent, asymptotically efficient and asymptotically normal. Examples and applications to conjugate families of densities, to inference in MARKOV Chains and other nonstandard cases illustrate results
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