Asymptotically optimal empirical bayes procedures for selecting good |
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Authors: | Mohamed Tahir Kamel Rekab |
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Institution: | 1. Department of Statistics , Temple University , Philadelphia, PA, 19122;2. Department of Applied Mathematics , Florida Institute of Technology , Melbourne, FL, 32901 |
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Abstract: | Let ∏1,…,∏k denote k independent populations, where a random observation from population ∏ i has a uniform distribution over the interval (0,θ i ) and θ i is a realization of a random variable having an unknown prior distribution G i . Population ∏ i is said to be a good population if θ i ≥θ0, where θ0 is a given, positive number. This paper provides a sequence of empirical Bayes procedures for selecting the good populationsamong ∏1,…,∏ k . It is shown that these procedures are asymptotically optimal and that the order of associated convergence rates is O(n-r/4) for some r, 0<r<2, where n is the number of accumulated past observations at hand |
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Keywords: | Asymptotically Optimal Bayes Risk Convergence Rates Empirical Bayes Selection Procedure Prior Distribution |
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