On Statistical Hypotheses Optimal Testing and Identification
Abstract
A new aspect of the in°uence of the information-theoretical methods on the statistical theory is considered. The procedures of the probability distributions identi¯cation for K(¸ 1) random objects each having one from the known set of M(¸ 2) distributions are studied. N-sequences of discrete independent random variables represent results of N observations for each of K objects. Decisions concerning probability distributions of the objects must be made on the base of such samples. For N ! 1 the exponential decrease of the test's error probabilities is considered. The reliability matrices of logarithmically asymptotically optimal procedures are explored for some models and formulations of the identi¯cation problems. The optimal subsets of reliabilities which values may be given beforehand and conditions guaranteeing positiveness of all the reliabilities are investigated.
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