Inference for the limiting cluster size distribution of extreme values

Details Inference for the limiting cluster size distribution of extreme values Inference for the limiting cluster size distribution of extreme values

2008-10-07

arxiv.org/abs/0810.1150v2

Annals of Statistics 2009, Vol. 37, No. 1, 271-310

Statistics

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Published in at http://dx.doi.org/10.1214/07-AOS551 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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