Inference for the limiting cluster size distribution of extreme values
Christian Y. Robert
Source: Ann. Statist. Volume 37, Number 1
(2009), 271-310.
Abstract
Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The underlying Poisson points represent the cluster positions and the multiplicities correspond to the cluster sizes. In the present paper we introduce estimators of the limiting cluster size probabilities, which are constructed through a recursive algorithm. We derive estimators of the extremal index which plays a key role in determining the intensity of cluster positions. We study the asymptotic properties of the estimators and investigate their finite sample behavior on simulated data.
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Keywords: Extreme values; exceedance point processes; limiting cluster size distribution; extremal index; strictly stationary sequences
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1232115935
Digital Object Identifier: doi:10.1214/07-AOS551
Mathematical Reviews number (MathSciNet): MR2488352
Zentralblatt MATH identifier: 1158.62061
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