Open Access
February 2009 Inference for the limiting cluster size distribution of extreme values
Christian Y. Robert
Ann. Statist. 37(1): 271-310 (February 2009). DOI: 10.1214/07-AOS551


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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Christian Y. Robert. "Inference for the limiting cluster size distribution of extreme values." Ann. Statist. 37 (1) 271 - 310, February 2009.


Published: February 2009
First available in Project Euclid: 16 January 2009

zbMATH: 1158.62061
MathSciNet: MR2488352
Digital Object Identifier: 10.1214/07-AOS551

Primary: 60G70 , 62E20 , 62M09
Secondary: 62G20 , 62G32

Keywords: exceedance point processes , extremal index , Extreme values , limiting cluster size distribution , strictly stationary sequences

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 1 • February 2009
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