Joint distributions of numbers of occurrences of a discrete pattern and weak convergence of an empirical process for the pattern

Sigeo Aki

Journal of Multivariate Analysis, 2008, vol. 99, issue 7, 1460-1473

Abstract: For a {0, 1}-pattern of finite length, an empirical process is introduced in order to describe the number of overlapping occurrences of the pattern at each level t[set membership, variant][0,1] in a sequence of the corresponding indicators of i.i.d. [0, 1]-valued observations of length n. A method for obtaining the exact finite-dimensional distributions of the empirical process is given. The weak convergence of the process to a Gaussian process in D[0,1] as n tends to infinity is also established. The limiting process depends on the given pattern. The exact covariance function is compared with the asymptotic covariance function in a numerical example.

Keywords: primary; 62G30 secondary; 62E20; 62E15 Run Pattern Type III binomial distribution of order k Empirical process Weak convergence Distribution theory (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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