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

Bortot, Paola; Coles, Stuart

Bernoulli, Tome 6 (2000) no. 6, p. 183-190 / Harvested from Project Euclid

Résumé

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.

Publié le : 2000-02-14
Classification: extreme value theory, kernel density estimation, Markov chain, random walk, sufficient statistics

@article{1082665385,
     author = {Bortot, Paola and Coles, Stuart},
     title = {A sufficiency property arising from the characterization of extremes of Markov chains},
     journal = {Bernoulli},
     volume = {6},
     number = {6},
     year = {2000},
     pages = { 183-190},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1082665385}
}

Bortot, Paola; Coles, Stuart. A sufficiency property arising from the characterization of extremes of Markov chains. Bernoulli, Tome 6 (2000) no. 6, pp.  183-190. http://gdmltest.u-ga.fr/item/1082665385/