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Teoriya Veroyatnostei i ee Primeneniya, 1982, Volume 27, Issue 2, Pages 369–373
(Mi tvp2363)
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This article is cited in 2 scientific papers (total in 2 papers)
Short Communications
More precise form of the central limit theorem for $U$-statistics of $m$-dependent variables
T. L. Malevič, В. Abdalimov Taškent
Abstract:
Let $X_1,X_2,\dots$ be a stationary sequence of $m$-dependent random variables and let $\Phi(x_1,\dots,x_r)$ be a symmetric function. For the distribution of the $U$-statistics
$$
U_n=(C_n^r)^{-1}\sum_{1\le i_1<\dots<i_r\le n}\Phi(X_{i_1},\dots,X_{i_r})
$$
the rate of convergence to the normal law is investigated.
Received: 20.07.1980
Citation:
T. L. Malevič, В. Abdalimov, “More precise form of the central limit theorem for $U$-statistics of $m$-dependent variables”, Teor. Veroyatnost. i Primenen., 27:2 (1982), 369–373; Theory Probab. Appl., 27:2 (1983), 391–396
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https://www.mathnet.ru/eng/tvp2363 https://www.mathnet.ru/eng/tvp/v27/i2/p369
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Abstract page: | 150 | Full-text PDF : | 92 |
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