Model misspecification in peaks over threshold analysis

Details Model misspecification in peaks over threshold analysis Model misspecification in peaks over threshold analysis

2010-10-07

arxiv.org/abs/1010.1357v1

Annals of Applied Statistics 2010, Vol. 4, No. 1, 203-221

Statistics

Applications

Published in at http://dx.doi.org/10.1214/09-AOAS292 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

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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