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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1966, Volume 11, Issue 2, Pages 306–313 (Mi tvp625)

Short Communications

Some generalizations of the empty boxes test

I. I. Viktorova, V. P. Chistyakov

Moscow

Abstract: Let us suppose that $n$ balls are distributed among $N$ boxes so that each ball may $N$ fall into the ith box with probability $a_i$ ($a_i\ge0$, $\sum_{i=1}^Na_i=1$) independently of what happens to the other balls. Let $\mu_r$ denote the number of boxes in which we have exactly $r$ balls. There are two hypotheses about $a_i$, $i=1,…,N$ approaching each other as $N$ increases. To distinguish these hypotheses statistical tests based on $\mu_0,\mu_1,…,\mu_r$ are considered. The most powerful test among the ones based on the linear statistics $\xi_r=c_{0r}\mu_0+…+c_{rr}\mu_r$ is found. This test is proved to coincide asymptotically with the Neyman–Pearson test e.g. it is the optimal one in the class of all the tests based on $\mu_0,\mu_1,…,\mu_r$.

Full text: PDF file (478 kB)

English version:
Theory of Probability and its Applications, 1966, 11:2, 270–276

Bibliographic databases:

Citation: I. I. Viktorova, V. P. Chistyakov, “Some generalizations of the empty boxes test”, Teor. Veroyatnost. i Primenen., 11:2 (1966), 306–313; Theory Probab. Appl., 11:2 (1966), 270–276

Citation in format AMSBIB
\Bibitem{VikChi66} \by I.~I.~Viktorova, V.~P.~Chistyakov \paper Some generalizations of the empty boxes test \jour Teor. Veroyatnost. i Primenen. \yr 1966 \vol 11 \issue 2 \pages 306--313 \mathnet{http://mi.mathnet.ru/tvp625} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=202248} \zmath{https://zbmath.org/?q=an:0161.38101} \transl \jour Theory Probab. Appl. \yr 1966 \vol 11 \issue 2 \pages 270--276 \crossref{https://doi.org/10.1137/1111021}