V. E. Bening, A. K. Gorshenin, V. Yu. Korolev, “An asymptotically optimal test for the number of components of a mixture of probability distributions”, Inform. Primen., 2011, Volume 5, Issue 3,Pages <nobr>4

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An asymptotically optimal test for the number of components of a mixture of probability distributions

V. E. Bening^ab, A. K. Gorshenin^ab, V. Yu. Korolev^ab

^a Institute for Problems of Informatics RAS
^b M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: The problem of statistical testing of hypotheses concerning the number of components in a mixture of probability distributions is considered. An asymptotically most powerful test is presented. Under rather weak conditions, the limit distributions, power loss, and the asymptotic deficiency are found. The application of this test to verification of hypotheses concerning the number of components in a mixture of uniform, normal, and gamma distributions is considered in detail.

Keywords: mixtures of probability distributions; asymptotically most powerful test; power loss; asymptotic deficiency.