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On an empirical Bayes test for a normal mean. (English) Zbl 1105.62301
Summary: We exhibit an empirical Bayes test \(\delta_n^*\) for the normal mean testing problem using a linear error loss. Under the condition that the critical point of a Bayes test is within some known compact interval, \(\delta_n^*\) is shown to be asymptotically optimal and its associated regret Bayes risk converges to zero at a rate \(O(n^{-1}(\ln n)^{1.5})\), where n is the number of past experiences available when the current component decision problem is considered. Under the same condition this rate is faster than the optimal rate of convergence claimed by Karunamuni.

62C12 Empirical decision procedures; empirical Bayes procedures
62F03 Parametric hypothesis testing
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