The Annals of Statistics

On the Asymptotic Behaviour of Empirical Bayes Tests for the Continuous One-Parameter Exponential Family

Theo Stijnen

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Abstract

Several authors have proposed empirical Bayes tests (EBT) for the continuous one-parameter exponential family for the case that the prior distribution is completely unspecified. They investigated the convergence rate of the (unconditional) Bayes risk, and gave upper bounds for this convergence rate. In this paper it is proposed to study the convergence of the conditional Bayes risk. A method is presented which makes it possible to derive the exact convergence rate of the conditional risk and its limit distribution. Several results are given. Also the question is considered whether monotonizing an empirical Bayes test influences its asymptotic properties.

Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 403-412.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346601

Digital Object Identifier
doi:10.1214/aos/1176346601

Mathematical Reviews number (MathSciNet)
MR773176

Zentralblatt MATH identifier
0588.62010

JSTOR
links.jstor.org

Subjects
Primary: 62C12: Empirical decision procedures; empirical Bayes procedures
Secondary: 62F05: Asymptotic properties of tests

Keywords
Empirical Bayes convergence rate conditional Bayes risk monotone test

Citation

Stijnen, Theo. On the Asymptotic Behaviour of Empirical Bayes Tests for the Continuous One-Parameter Exponential Family. Ann. Statist. 13 (1985), no. 1, 403--412. doi:10.1214/aos/1176346601. https://projecteuclid.org/euclid.aos/1176346601


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