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 Diskr. Mat., 2001, Volume 13, Issue 4, Pages 52–59 (Mi dm301)

A chi-square statistic based on the chains of outcomes of independent trials with gaps

V. P. Chistyakov

Abstract: The detection of dependences in random sequences in the cases, where the dependence makes itself evident only on frequencies of long tuples of outcomes, involves difficulties connected with bounded possibilities of computers. In this case, the use is made of different criteria based on statistics depending on long tuples of successive symbols in the sequence under consideration or on incomplete tuples of symbols separated from each other. The criteria of such type can be found in [1]. In this paper, we find the limit distributions of chi-square statistics based on incomplete tuples of outcomes of independent trials in the case, where the number of trials tends to infinity, the outcomes are equiprobable, and the number of outcomes is finite.
This research was supported by the Russian Foundation of Basic Research, grant 99–01–00012, and by the Council for State Support of Leading Scientific Schools, grant 00–15–96136.

DOI: https://doi.org/10.4213/dm301

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English version:
Discrete Mathematics and Applications, 2001, 11:5, 485–492

Bibliographic databases:

UDC: 519.2

Citation: V. P. Chistyakov, “A chi-square statistic based on the chains of outcomes of independent trials with gaps”, Diskr. Mat., 13:4 (2001), 52–59; Discrete Math. Appl., 11:5 (2001), 485–492

Citation in format AMSBIB
\Bibitem{Chi01} \by V.~P.~Chistyakov \paper A~chi-square statistic based on the chains of outcomes of independent trials with gaps \jour Diskr. Mat. \yr 2001 \vol 13 \issue 4 \pages 52--59 \mathnet{http://mi.mathnet.ru/dm301} \crossref{https://doi.org/10.4213/dm301} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1901782} \zmath{https://zbmath.org/?q=an:1135.62308} \transl \jour Discrete Math. Appl. \yr 2001 \vol 11 \issue 5 \pages 485--492 

• http://mi.mathnet.ru/eng/dm301
• https://doi.org/10.4213/dm301
• http://mi.mathnet.ru/eng/dm/v13/i4/p52

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This publication is cited in the following articles:
1. M. I. Tikhomirova, V. P. Chistyakov, “On two chi-square-type statistics constructed from the frequencies of tuples of states of a multiple Markov chain”, Discrete Math. Appl., 13:3 (2003), 319–329
2. M. I. Tikhomirova, V. P. Chistyakov, “On some $\chi^2$-type statistics that depend functionally on estimators of unknown parameters”, Discrete Math. Appl., 15:1 (2005), 33–46
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