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Teoriya Veroyatnostei i ee Primeneniya, 1975, Volume 20, Issue 1, Pages 115–125
(Mi tvp2993)
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This article is cited in 2 scientific papers (total in 2 papers)
Estimation of necessary sample size for testing simple close hypotheses
È. V. Khmaladze Institute of Economics and Law, Academy of Science, Georgian SSR
Abstract:
Let $F_{1_n}$ and $F_{2_n}$ be the $n$-times direct products of distributions $F_1$ and $F_2$ correspondingly. The problem of estimation of necessary sample size for testing hypothesis $F_1$ against $F_2$ is represented as the problem of estimation $\nu=\min\{n\colon\operatorname{var}(F_{1_n},F_{2_n})\ge u=\mathrm{const}\}$. The upper and lower bounds for $\nu$ are given and, supposing $\operatorname{var}(F_{1_n},F_{2_n})\to0$, the asymptotically equivalent estimations for $\nu$ are described in terms of semigroups of limit distributions of $L=\sum\ln[dF_2(X_i)/dF_1(X_i)]$.
Received: 31.01.1974
Citation:
È. V. Khmaladze, “Estimation of necessary sample size for testing simple close hypotheses”, Teor. Veroyatnost. i Primenen., 20:1 (1975), 115–125; Theory Probab. Appl., 20:1 (1975), 116–126
Linking options:
https://www.mathnet.ru/eng/tvp2993 https://www.mathnet.ru/eng/tvp/v20/i1/p115
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