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 Diskr. Mat., 2000, Volume 12, Issue 4, Pages 46–52 (Mi dm349)

Moving chi-square

M. I. Tikhomirova, V. P. Chistyakov

Abstract: A sequence of independent identically distributed random variables taking values from the set $\{1,2,…,N\}$ are partitioned into disjoint intervals of length $n$, and $s$ sequential intervals beginning with the $t$th interval form the $t$th sample of size $ns$. It is proved that if $n\to\infty$ and $N$, $r$ are fixed, then the joint $r$-dimensional distribution of $\chi^2$-statistics constructed for samples of sizes $ns$ with numbers $t_1<t_2<…<t_r$ converges to some limit distribution. For this limit distribution, a Gaussian approximation is given.
The work was supported by the Russian Foundation for Basic Research, grant 00–15–96136.

DOI: https://doi.org/10.4213/dm349

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English version:
Discrete Mathematics and Applications, 2000, 10:5, 469–475

Bibliographic databases:

UDC: 519.2

Citation: M. I. Tikhomirova, V. P. Chistyakov, “Moving chi-square”, Diskr. Mat., 12:4 (2000), 46–52; Discrete Math. Appl., 10:5 (2000), 469–475

Citation in format AMSBIB
\Bibitem{TikChi00} \by M.~I.~Tikhomirova, V.~P.~Chistyakov \paper Moving chi-square \jour Diskr. Mat. \yr 2000 \vol 12 \issue 4 \pages 46--52 \mathnet{http://mi.mathnet.ru/dm349} \crossref{https://doi.org/10.4213/dm349} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1826178} \zmath{https://zbmath.org/?q=an:0973.60043} \transl \jour Discrete Math. Appl. \yr 2000 \vol 10 \issue 5 \pages 469--475 

• http://mi.mathnet.ru/eng/dm349
• https://doi.org/10.4213/dm349
• http://mi.mathnet.ru/eng/dm/v12/i4/p46

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. B. I. Selivanov, “A family of multivariate chi-square statistics”, Discrete Math. Appl., 12:4 (2002), 401–413
2. B. I. Selivanov, “A family of multivariate $\chi^2$-statistics”, Discrete Math. Appl., 14:5 (2004), 527–533
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