Journal of Mathematical Sciences

, Volume 189, Issue 6, pp 967–975 | Cite as

On the asymptotic defect of some Bayesian criteria*

  • V. E. BeningEmail author

This paper focuses on the problem of testing a simple hypothesis about a one-dimensional parameter against one-sided alternatives with independent identically distributed random variables. A formula for extreme deviation of the power function from the envelope power function is obtained for asymptotically efficient Bayesian criteria based on a Bayesian likelihood ratio. This formula makes it possible to find the asymptotic deficiency in terms of the Hodges–Lehmann deficiency. The method used here makes it possible to relax necessary regularity conditions.


Asymptotic Expansion Regularity Condition Nuisance Parameter Extreme Deviation Simple Hypothesis 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia

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