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Teoriya Veroyatnostei i ee Primeneniya, 2006, Volume 51, Issue 4, Pages 712–731
DOI: https://doi.org/10.4213/tvp21 (Mi tvp21) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Pattern correlation matrices for Markov sequences and tests of randomness

A. L. Rukhinab

a Department of Mathematics and Statistics, University of Maryland, Baltimore County
b National Institute of Standards and Technology
Full-text PDF (1604 kB) Citations (6)
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DOI: https://doi.org/10.4213/tvp21
Abstract: The paper establishes some properties of the so-called pattern correlation matrices which are useful in statistical analysis of random Markov sequences. Asymptotic expansions for the probability of the occurrence of a given word a given number of times and of joint occurrences for two words are derived. These expansions give accurate approximations for the first two moments of the number of occurrences. The covariance matrix of the joint distribution of frequencies of all patterns is expressed in terms of the pattern correlation matrix, and a simple generalized inverse of this covariance matrix is given. Relevant statistical implications for goodness-of-fit testing are formulated.
Keywords: asymptotic expansions, resolvent, generating function, pseudo-inverse matrix, $\chi$-square, fundamental matrix.
Received: 30.09.2005
English version:
Theory of Probability and its Applications, 2007, Volume 51, Issue 4, Pages 663–679
DOI: https://doi.org/10.1137/S0040585X97982670
Bibliographic databases:
Language: Russian
Citation: A. L. Rukhin, “Pattern correlation matrices for Markov sequences and tests of randomness”, Teor. Veroyatnost. i Primenen., 51:4 (2006), 712–731; Theory Probab. Appl., 51:4 (2007), 663–679
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
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