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

This article is cited in 2 scientific papers (total in 2 papers)

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

Full text: PDF file (420 kB)
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English version:
Discrete Mathematics and Applications, 2000, 10:5, 469–475

Bibliographic databases:

UDC: 519.2
Received: 03.05.2000

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


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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. B. I. Selivanov, “A family of multivariate chi-square statistics”, Discrete Math. Appl., 12:4 (2002), 401–413  mathnet  crossref  mathscinet  zmath
    2. B. I. Selivanov, “A family of multivariate $\chi^2$-statistics”, Discrete Math. Appl., 14:5 (2004), 527–533  mathnet  crossref  crossref  mathscinet  zmath
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