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Teoriya Veroyatnostei i ee Primeneniya, 1979, Volume 24, Issue 3, Pages 637–645
(Mi tvp2654)
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This article is cited in 3 scientific papers (total in 3 papers)
Short Communications
Lower bounds for average sample size in the tests of goodness-of-fit and homogeneity
I. N. Volodin Kazan'
Abstract:
The problems of testing hypothesis $P=P_0$ on the distribution $P$ of random variable $\xi$ against the class of alternatives
$$
\mathscr P_1=\{P\colon \sup_A|P(A)-P_0(A)|\ge\Delta\}
$$
and of testing hypothesis $P_1=P_2$ on the distributions $P_1$ and $P_2$ of independent random variables $\xi$ and $\eta$ against the class of alternatives
$$
\mathscr P_2=\{(P_1,P_2)\colon \sup_A|P_1(A)-P_2(A)|\ge\Delta\}
$$
are considered. Lower bounds for average sample size which is sufficient for the acceptance of decision with guaranted restrictions $(\alpha,\beta)$ on the probabilities of errors are established. The asymptotical (for $\Delta\to 0$) efficiency of Kolmogorov and Smirnov tests with respect to obtained bounds is investigated.
Received: 09.07.1977
Citation:
I. N. Volodin, “Lower bounds for average sample size in the tests of goodness-of-fit and homogeneity”, Teor. Veroyatnost. i Primenen., 24:3 (1979), 637–645; Theory Probab. Appl., 24:3 (1980), 640–649
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https://www.mathnet.ru/eng/tvp2654 https://www.mathnet.ru/eng/tvp/v24/i3/p637
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Abstract page: | 197 | Full-text PDF : | 101 | First page: | 1 |
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