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Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 3, Pages 569–575 (Mi tvp742)  

Short Communications

On statistical tests for a simple hypotheses in the case of multy-dimensional normal distribution

A. E. Zaslavskii

Novosibirsk State University

Abstract: The optimal statistical test for the choice of one of two simple hypothesis in the case of multi-dimensional normal distribution is very complicated in practical applications. One can construct a simplified test neglecting the dependence of the components of the normal variate. In this paper the difference between the probabilities of the second kind errors of the optimal and simplified tests is investigated. A necessary and sufficient condition for this difference to be equal to zero as well as some estimates, of this difference are given. The case when the parameters of the normal distribution are a priori unknown is considered separately.

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English version:
Theory of Probability and its Applications, 1967, 12:3, 514–519

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Received: 04.05.1966

Citation: A. E. Zaslavskii, “On statistical tests for a simple hypotheses in the case of multy-dimensional normal distribution”, Teor. Veroyatnost. i Primenen., 12:3 (1967), 569–575; Theory Probab. Appl., 12:3 (1967), 514–519

Citation in format AMSBIB
\Bibitem{Zas67}
\by A.~E.~Zaslavskii
\paper On statistical tests for a~simple hypotheses in the case of multy-dimensional normal distribution
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 3
\pages 569--575
\mathnet{http://mi.mathnet.ru/tvp742}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=220398}
\zmath{https://zbmath.org/?q=an:0168.39702}
\transl
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 3
\pages 514--519
\crossref{https://doi.org/10.1137/1112065}


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