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Short asymptotic expansions in the CLT in Euclidean spaces: a sharp estimate for its accuracyстатья
- Авторы: Ulyanov V.V., Götze F.
- Сборник: Proceedings 2011 World Congress on Engineering and Technology, vol. 1, 28 Oct–2 Nov 2011, Shanghai, China
- Том: 1
- Год издания: 2011
- Место издания: IEEE
- Первая страница: 260
- Последняя страница: 262
- Аннотация: We prove sharp bounds for remainder terms in short asymptotic expansions in the central limit theorem for sums of independent identically distributed random elements in a Hilbert space H. Our bounds of order O(1/n) depend on the first twelve eigenvalues of the covariance operator of a summand only. We provide lower bounds which show that this number of eigenvalues is best possible. Moreover, the forms of dependence on the eigenvalues of covariance operator of a summand coincide in upper and lower bounds.
- Добавил в систему: Ульянов Владимир Васильевич