publication . Article . Other literature type . 2000

a sufficiency property arising from the characterization of extremes of markov chains

Bortot, Paola; Coles, Stuart;
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  • Published: 01 Feb 2000 Journal: Bernoulli, volume 6, page 183 (issn: 1350-7265, Copyright policy)
  • Publisher: JSTOR
Abstract
At extreme levels, it is known that for a particular choice of marginal distribution, transitions of a Markov chain behave like a random walk. For a broad class of Markov chains, we give a characterization for the step length density of the limiting random walk, which leads to an interesting sufficiency property. This representation also leads us to propose a new technique for kernel density estimation for this class of models.
Subjects
free text keywords: Statistics and Probability, Markov model, Markov chain mixing time, Random walk, Variable-order Markov model, Markov kernel, Statistics, Markov property, Markov chain, Mathematics, Markov renewal process, extreme value theory, kernel density estimation, sufficient statistics
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