Summary
We consider the empirical Bayes solution in such a situation where the sample size is successively determined by a rule which includes the Bayes risks and the observation costs. The empirical Bayes floating optimal sample size depends on current as well as on previous information assumed to be collected from earlier performances of similar decisions. The sampling is done from an exponential conditional distribution, with a single parameter. The proofs, which show the asymptotic optimality of the empirical Bayes solution, are presented for a hypotheses-testing problem. A straight generalization to a multiple decision problem is also given.
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Laippala, P. The empirical bayes rules with floating optimal sample size for exponential conditional distributions. Ann Inst Stat Math 37, 315–327 (1985). https://doi.org/10.1007/BF02481100
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DOI: https://doi.org/10.1007/BF02481100