The Annals of Statistics
- Ann. Statist.
- Volume 37, Number 1 (2009), 1-568
Inference for the limiting cluster size distribution of extreme values
Full-text: Open access
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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