Estimating the Extremal Index. Smith, R. L. & Weissman, I. Journal of the Royal Statistical Society. Series B (Methodological), 56(3):pp. 515-528, Wiley for the Royal Statistical Society, 1994. ![Estimating the Extremal Index [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper abstract bibtex The extremal index is an important parameter measuring the degree of clustering of extremes in a stationary process. If we consider the point process of exceedance times over a high threshold, then this can be shown to converge asymptotically to a clustered Poisson process. The extremal index, a parameter in the interval [0,1], is the reciprocal of the mean cluster size. Apart from being of interest in its own right, it is a crucial parameter for determining the limiting distribution of extreme values from the process. In this paper we review current work on statistical estimation of the extremal index and consider an optimality criterion based on a bias-variance trade-off. Theoretical results are developed for a simple doubly stochastic process, and it is argued that the main formula obtained is valid for a much wider class of processes. The practical implications are examined through simulations and a real data example.
@article{ 1994,
abstract = {The extremal index is an important parameter measuring the degree of clustering of extremes in a stationary process. If we consider the point process of exceedance times over a high threshold, then this can be shown to converge asymptotically to a clustered Poisson process. The extremal index, a parameter in the interval [0,1], is the reciprocal of the mean cluster size. Apart from being of interest in its own right, it is a crucial parameter for determining the limiting distribution of extreme values from the process. In this paper we review current work on statistical estimation of the extremal index and consider an optimality criterion based on a bias-variance trade-off. Theoretical results are developed for a simple doubly stochastic process, and it is argued that the main formula obtained is valid for a much wider class of processes. The practical implications are examined through simulations and a real data example.},
added-at = {2013-05-31T11:03:35.000+0200},
author = {Smith, Richard L. and Weissman, Ishay},
biburl = {http://www.bibsonomy.org/bibtex/2c8d8887a22bed11d75f817afa6f19aee/marsianus},
copyright = {Copyright © 1994 Royal Statistical Society},
description = {JSTOR: Journal of the Royal Statistical Society. Series B (Methodological), Vol. 56, No. 3 (1994), pp. 515-528},
interhash = {f73485c22e00e96463349e4d8a04b8ca},
intrahash = {c8d8887a22bed11d75f817afa6f19aee},
issn = {00359246},
journal = {Journal of the Royal Statistical Society. Series B (Methodological)},
jstor_articletype = {research-article},
jstor_formatteddate = {1994},
keywords = {Dependence extremalIndex},
language = {English},
number = {3},
pages = {pp. 515-528},
publisher = {Wiley for the Royal Statistical Society},
title = {Estimating the Extremal Index},
url = {http://www.jstor.org/stable/2346124},
volume = {56},
year = {1994}
}
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