RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Journal history Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

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

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

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} 

• http://mi.mathnet.ru/eng/fpm184
• http://mi.mathnet.ru/eng/fpm/v2/i4/p999

 SHARE:

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
2. Bulinski A., Suquet C., “Normal approximation for quasi-associated random fields”, Statistics & Probability Letters, 54:2 (2001), 215–226
3. A. P. Shashkin, “A Berry–Esseen Type Estimate for a Weakly Associated Vector Random Field”, Math. Notes, 72:4 (2002), 569–575
4. A. V. Bulinski, “Statistical Version of the Central Limit Theorem for Vector-Valued Random Fields”, Math. Notes, 76:4 (2004), 455–464
5. A. V. Lebedev, “Maximal branching processes with non-negative values”, Theory Probab. Appl., 50:3 (2006), 482–488
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
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
8. E. A. Savinov, “Predelnaya teorema dlya kopul preobrazovanii nezavisimosti $t$-raspredeleniya Styudenta”, Vestn. SamGU. Estestvennonauchn. ser., 2011, no. 8(89), 69–85
9. A. P. Shashkin, “Asymptotic normality of estimates with local averaging for weakly dependent random fields”, Theory Probab. Appl., 59:3 (2015), 516–526
•  Number of views: This page: 333 Full text: 127 First page: 2