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Mat. Tr., 2004, Volume 7, Number 1, Pages 91–152 (Mi mt72)  

This article is cited in 3 scientific papers (total in 3 papers)

On the Accuracy of Gaussian Approximation in Hilbert Space

S. V. Nagaeva, V. I. Chebotarevb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Computer Centre Far-Eastern Branch of RAS

Abstract: This article is a continuation of the authors' paper [1] with a new approach to studying the accuracy of order $O(1/n)$ of Gaussian approximation in Hilbert space. In contrast to [1], we now study a more general case of the class of sets on which the probability measures are compared, namely, the class of balls with arbitrary centers. The resultant bound depends on the thirteen greatest eigenvalues of the covariance operator $T$ in explicit form; moreover, this dependence is sharper as compared to the bound of [2].

Key words: Gaussian approximation in Hilbert space, eigenvalues of the covariance operator, discretization of a probability distribution, conditionally independent random variables.

Full text: PDF file (3724 kB)
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English version:
Siberian Advances in Mathematics, 2005, 15:1, 11–73

Bibliographic databases:

UDC: 519.214.4
Received: 10.06.2002

Citation: S. V. Nagaev, V. I. Chebotarev, “On the Accuracy of Gaussian Approximation in Hilbert Space”, Mat. Tr., 7:1 (2004), 91–152; Siberian Adv. Math., 15:1 (2005), 11–73

Citation in format AMSBIB
\Bibitem{NagChe04}
\by S.~V.~Nagaev, V.~I.~Chebotarev
\paper On the~Accuracy of~Gaussian Approximation in Hilbert Space
\jour Mat. Tr.
\yr 2004
\vol 7
\issue 1
\pages 91--152
\mathnet{http://mi.mathnet.ru/mt72}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2068278}
\zmath{https://zbmath.org/?q=an:1125.60300}
\elib{https://elibrary.ru/item.asp?id=9530095}
\transl
\jour Siberian Adv. Math.
\yr 2005
\vol 15
\issue 1
\pages 11--73


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. F. Götze, A. Yu. Zaitsev, “Uniform rates of approximation by short asymptotic expansions in the CLT for quadratic forms”, J. Math. Sci. (N. Y.), 176:2 (2011), 162–189  mathnet  crossref
    2. Goetze F., Zaitsev A.Yu., “Explicit Rates of Approximation in the Clt for Quadratic Forms”, Ann. Probab., 42:1 (2014), 354–397  crossref  mathscinet  zmath  isi  scopus
    3. Jirak M., “Rate of Convergence For Hilbert Space Valued Processes”, Bernoulli, 24:1 (2018), 202–230  crossref  mathscinet  zmath  isi  scopus
  • Математические труды Siberian Advances in Mathematics
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