Annals of Applied Statistics

Model misspecification in peaks over threshold analysis

Mária Süveges and Anthony C. Davison

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Abstract

Classical peaks over threshold analysis is widely used for statistical modeling of sample extremes, and can be supplemented by a model for the sizes of clusters of exceedances. Under mild conditions a compound Poisson process model allows the estimation of the marginal distribution of threshold exceedances and of the mean cluster size, but requires the choice of a threshold and of a run parameter, K, that determines how exceedances are declustered. We extend a class of estimators of the reciprocal mean cluster size, known as the extremal index, establish consistency and asymptotic normality, and use the compound Poisson process to derive misspecification tests of model validity and of the choice of run parameter and threshold. Simulated examples and real data on temperatures and rainfall illustrate the ideas, both for estimating the extremal index in nonstandard situations and for assessing the validity of extremal models.

Article information

Source
Ann. Appl. Stat., Volume 4, Number 1 (2010), 203-221.

Dates
First available in Project Euclid: 11 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1273584453

Digital Object Identifier
doi:10.1214/09-AOAS292

Mathematical Reviews number (MathSciNet)
MR2758170

Zentralblatt MATH identifier
1189.62086

Keywords
Cluster extremal index extreme value theory likelihood model misspecification Neuchâtel temperature data Venezuelan rainfall data

Citation

Süveges, Mária; Davison, Anthony C. Model misspecification in peaks over threshold analysis. Ann. Appl. Stat. 4 (2010), no. 1, 203--221. doi:10.1214/09-AOAS292. https://projecteuclid.org/euclid.aoas/1273584453


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