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Biometrika 1968 55(1):83-100; doi:10.1093/biomet/55.1.83
© 1968 by Biometrika Trust
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On the smooth empirical Bayes approach to testing of hypotheses and the compound decision problem

J. S. MARITZ

University of Melbourne Victoria, Australia

The smooth empirical Bayes approach is based on using past observations to estimate a specified type of approximation to the prior distribution. This approach is applied to problems of empirical Bayes hypothesis testing and to the compound decision problem. Problems involving composite hypotheses are considered which have, hitherto, received much less attention than the case of two simple hypotheses. The methods are shown to be asymptotically optimal and results of studies involving finite sample numbers are reported, giving some indication of the rate of approach to optimality in specific cases.


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