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Fundam. Prikl. Mat., 1996, Volume 2, Issue 4, Pages 999–1018 (Mi fpm184)  

This article is cited in 9 scientific papers (total in 9 papers)

Research Papers Dedicated to the Memory of B. V. Gnedenko

Statistical variant of the CLT for associated random fields

A. V. Bulinski, M. A. Vronskii

M. V. Lomonosov Moscow State University

Abstract: The asymptotic normality of sums taken over the “regulary”growing subsets of $\mathbf Z^{d}$ is studied for a strictly stationary associated random field $\{X_{j}, j\in\mathbf Z^{d}\}$, $d\geq1$. In this connection families of random normalizations are introduced which permits us to construct approximate confidence intervals for the unknown mean of the field. These normalizations include the two statistics proposed for processes (i.e. $d=1$) in a recent paper by M. Peligrad and Q.-M. Shao.

Full text: PDF file (659 kB)

Bibliographic databases:
UDC: 519.21
Received: 01.02.1996

Citation: A. V. Bulinski, M. A. Vronskii, “Statistical variant of the CLT for associated random fields”, Fundam. Prikl. Mat., 2:4 (1996), 999–1018

Citation in format AMSBIB
\Bibitem{BulVro96}
\by A.~V.~Bulinski, M.~A.~Vronskii
\paper Statistical variant of the CLT for associated random fields
\jour Fundam. Prikl. Mat.
\yr 1996
\vol 2
\issue 4
\pages 999--1018
\mathnet{http://mi.mathnet.ru/fpm184}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1785768}
\zmath{https://zbmath.org/?q=an:0902.60025}


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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. M. A. Vronskii, “Refinement of the almost sure central limit theorem for associated processes”, Math. Notes, 68:4 (2000), 444–451  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Bulinski A., Suquet C., “Normal approximation for quasi-associated random fields”, Statistics & Probability Letters, 54:2 (2001), 215–226  crossref  mathscinet  zmath  isi
    3. A. P. Shashkin, “A Berry–Esseen Type Estimate for a Weakly Associated Vector Random Field”, Math. Notes, 72:4 (2002), 569–575  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. A. V. Bulinski, “Statistical Version of the Central Limit Theorem for Vector-Valued Random Fields”, Math. Notes, 76:4 (2004), 455–464  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. A. V. Lebedev, “Maximal branching processes with non-negative values”, Theory Probab. Appl., 50:3 (2006), 482–488  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Bulinski A., “Central Limit Theorem for Random Fields and Applications”, Advances in Data Analysis - Theory and Applications to Reliability and Inference, Data Mining, Bioinformatics, Lifetime Data, and Neural Networks, Statistics for Industry and Technology, 2010, 141–150  mathscinet  isi
    7. Bulinskii A.V., “Tsentralnaya predelnaya teorema dlya polozhitelno assotsiirovannykh statsionarnykh sluchainykh polei”, Vestnik Sankt-Peterburgskogo universiteta. Seriya 1: Matematika. Mekhanika. Astronomiya, 2011, no. 2, 5–13  mathscinet  elib
    8. E. A. Savinov, “Predelnaya teorema dlya kopul preobrazovanii nezavisimosti $t$-raspredeleniya Styudenta”, Vestn. SamGU. Estestvennonauchn. ser., 2011, no. 8(89), 69–85  mathnet  elib
    9. A. P. Shashkin, “Asymptotic normality of estimates with local averaging for weakly dependent random fields”, Theory Probab. Appl., 59:3 (2015), 516–526  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Фундаментальная и прикладная математика
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