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March 2010 Model misspecification in peaks over threshold analysis
Mária Süveges, Anthony C. Davison
Ann. Appl. Stat. 4(1): 203-221 (March 2010). DOI: 10.1214/09-AOAS292


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.


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Mária Süveges. Anthony C. Davison. "Model misspecification in peaks over threshold analysis." Ann. Appl. Stat. 4 (1) 203 - 221, March 2010.


Published: March 2010
First available in Project Euclid: 11 May 2010

zbMATH: 1189.62086
MathSciNet: MR2758170
Digital Object Identifier: 10.1214/09-AOAS292

Keywords: cluster , extremal index , Extreme value theory , likelihood , model misspecification , Neuchâtel temperature data , Venezuelan rainfall data

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.4 • No. 1 • March 2010
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