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.
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