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 Diskr. Mat., 1997, Volume 9, Issue 4, Pages 127–136 (Mi dm501)

The sequential chi-square test based on $s$-tuples of states of a Markov chain

B. I. Selivanov, V. P. Chistyakov

Abstract: A multidimensional statistic whose components are one-dimensional chi-square statistics based on frequencies of outcomes of a sequence of multinomial trials was considered previously and the density of the limit distribution of this statistic was found. We extend this result to statistics based on $s$-tuples of states of a finite homogeneous Markov chain.
The research was supported by the Russian Foundation for Basic Research, grant 96-01-00531.

DOI: https://doi.org/10.4213/dm501

Full text: PDF file (778 kB)

English version:
Discrete Mathematics and Applications, 1997, 7:5, 523–532

Bibliographic databases:

UDC: 519.2

Citation: B. I. Selivanov, V. P. Chistyakov, “The sequential chi-square test based on $s$-tuples of states of a Markov chain”, Diskr. Mat., 9:4 (1997), 127–136; Discrete Math. Appl., 7:5 (1997), 523–532

Citation in format AMSBIB
\Bibitem{SelChi97} \by B.~I.~Selivanov, V.~P.~Chistyakov \paper The sequential chi-square test based on $s$-tuples of states of a Markov chain \jour Diskr. Mat. \yr 1997 \vol 9 \issue 4 \pages 127--136 \mathnet{http://mi.mathnet.ru/dm501} \crossref{https://doi.org/10.4213/dm501} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1629617} \zmath{https://zbmath.org/?q=an:0979.62056} \transl \jour Discrete Math. Appl. \yr 1997 \vol 7 \issue 5 \pages 523--532 

• http://mi.mathnet.ru/eng/dm501
• https://doi.org/10.4213/dm501
• http://mi.mathnet.ru/eng/dm/v9/i4/p127

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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. V. P. Chistyakov, “A chi-square statistic based on the chains of outcomes of independent trials with gaps”, Discrete Math. Appl., 11:5 (2001), 485–492
2. 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
3. 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
4. M. I. Tikhomirova, “Some characteristics of dependencies in discrete random sequences”, Discrete Math. Appl., 18:2 (2008), 173–180
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