• Bernoulli
  • Volume 6, Number 1 (2000), 183-190.

A sufficiency property arising from the characterization of extremes of Markov chains

Paola Bortot and Stuart Coles

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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.

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Bernoulli, Volume 6, Number 1 (2000), 183-190.

First available in Project Euclid: 22 April 2004

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extreme value theory kernel density estimation Markov chain random walk sufficient statistics


Bortot, Paola; Coles, Stuart. A sufficiency property arising from the characterization of extremes of Markov chains. Bernoulli 6 (2000), no. 1, 183--190.

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