The Annals of Statistics

Inference for the limiting cluster size distribution of extreme values

Christian Y. Robert

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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.

Article information

Source
Ann. Statist. Volume 37, Number 1 (2009), 271-310.

Dates
First available: 16 January 2009

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

Subjects
Primary: 60G70: Extreme value theory; extremal processes 62E20: Asymptotic distribution theory 62M09: Non-Markovian processes: estimation
Secondary: 62G20: Asymptotic properties 62G32: Statistics of extreme values; tail inference

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

Citation

Robert, Christian Y. Inference for the limiting cluster size distribution of extreme values. The Annals of Statistics 37 (2009), no. 1, 271--310. doi:10.1214/07-AOS551. http://projecteuclid.org/euclid.aos/1232115935.


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