The Annals of Statistics
- Ann. Statist.
- Volume 13, Number 1 (1985), 403-412.
On the Asymptotic Behaviour of Empirical Bayes Tests for the Continuous One-Parameter Exponential Family
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.
Ann. Statist., Volume 13, Number 1 (1985), 403-412.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62C12: Empirical decision procedures; empirical Bayes procedures
Secondary: 62F05: Asymptotic properties of tests
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