On a monotone empirical Bayes test in a positive exponential family |
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Authors: | TaChen Liang |
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Institution: | 1. Department of Mathematics, Wayne State University, Detroit, USA
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Abstract: | This paper studies a monotone empirical Bayes test δ n * for testing H 0:θ≤θ 0 against H 1:θ>θ 0 for the positive exponential family f(x|θ)=c(θ)u(x)exp?(?x/θ), x>0, using a weighted quadratic error loss. We investigate the convergence rate of the empirical Bayes test δ n * . It is shown that the regret of δ n * converges to zero at a rate O(n ?1), where n is the number of past data available when the present testing problem is considered. Errors regarding the rate of convergence claimed in Gupta and Li (J. Stat. Plan. Inference, 129: 3–18, 2005) are addressed. |
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