NDLI: Pattern Correlation Matrices for Markov Sequences and Tests of Randomness

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Rukhin, A. L.
Copyright Year	2007
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.
Starting Page	663
Ending Page	679
Page Count	17
File Format	PDF
ISSN	0040585X
DOI	10.1137/S0040585X97982670
e-ISSN	10957219
Journal	Theory of Probability & Its Applications (TPRBAU)
Issue Number	4
Volume Number	51
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2007-11-19
Access Restriction	Subscribed
Subject Keyword	fundamental matrix asymptotic expansions generating function resolvent pseudo-inverse matrix $\chi$-square
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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Pattern Correlation Matrices for Markov Sequences and Tests of Randomness