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Teor. Veroyatnost. i Primenen., 1976, Volume 21, Issue 1, Pages 34–47 (Mi tvp3273)  

On asymptotically optimal tests for composite hypotheses under non-standard conditions

A. V. Bernšteĭn

Moscow

Abstract: Let $X_1,…,X_n$ be independent identically distributed random variables from a distribution dependent on the parameters $\theta=(\theta_1,…,\theta_m)$ and $\xi$. The hypothesis $H_0\colon\xi=0$ is to be tested against the alternative $\xi>0$.
In [1], optimal asymptotic tests were obtained under the condition that the logarithmic derivatives of the density with respect to $\theta_r$, $r=1,…,m$, and $\xi$ at the point $\xi=0$ are linearly independent. In this paper, optimal asymptotic tests are constructed in the case when this condition is not satisfied. Also some results are obtained for the usual $C(\alpha)$-tests.

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English version:
Theory of Probability and its Applications, 1976, 21:1, 34–47

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Received: 24.12.1974

Citation: A. V. Bernšteǐn, “On asymptotically optimal tests for composite hypotheses under non-standard conditions”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 34–47; Theory Probab. Appl., 21:1 (1976), 34–47

Citation in format AMSBIB
\Bibitem{Ber76}
\by A.~V.~Bern{\v s}te{\v\i}n
\paper On asymptotically optimal tests for composite hypotheses under non-standard conditions
\jour Teor. Veroyatnost. i Primenen.
\yr 1976
\vol 21
\issue 1
\pages 34--47
\mathnet{http://mi.mathnet.ru/tvp3273}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=405673}
\zmath{https://zbmath.org/?q=an:0375.62074}
\transl
\jour Theory Probab. Appl.
\yr 1976
\vol 21
\issue 1
\pages 34--47
\crossref{https://doi.org/10.1137/1121003}


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