Bernoulli

  • 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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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.

Article information

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

Dates
First available in Project Euclid: 22 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1082665385

Mathematical Reviews number (MathSciNet)
MR1781187

Zentralblatt MATH identifier
0955.60059

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

Citation

Bortot, Paola; Coles, Stuart. A sufficiency property arising from the characterization of extremes of Markov chains. Bernoulli 6 (2000), no. 1, 183--190. https://projecteuclid.org/euclid.bj/1082665385


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References

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