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Teoriya Veroyatnostei i ee Primeneniya, 1976, Volume 21, Issue 1, Pages 34–47
(Mi tvp3273)
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This article is cited in 7 scientific papers (total in 7 papers)
On asymptotically optimal tests for composite hypotheses under non-standard conditions
A. V. Bernšteĭn Moscow
Abstract:
Let $X_1,\dots,X_n$ be independent identically distributed random variables from a distribution dependent on the parameters $\theta=(\theta_1,\dots,\theta_m)$ 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 $\theta_r$, $r=1,\dots,m$, 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.
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
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https://www.mathnet.ru/eng/tvp3273 https://www.mathnet.ru/eng/tvp/v21/i1/p34
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Abstract page: | 151 | Full-text PDF : | 73 |
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