Model misspecification in peaks over threshold analysis

By M. Suveges, A. C. Davison. 2010

64 citations recorded by the source corpus.

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.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/667b859370bcceaab359f19af9ef73926422c2a4

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Citations in the corpus

Modelling Time Series Extremes (2012, background): “It can also be used to diagnose inappropriate thresholds (Süveges and Davison, 2010).”
An efficient semiparametric maxima estimator of the extremal index (2015, methodology): “Recent advances in the estimation of θ (Ferro and Segers, 2003; Süveges, 2007; Süveges and Davison, 2010; Laurini and Tawn, 2003; Robert, 2013) have concentrated on threshold methods, based on exceedences of a threshold.”
Cross‐validatory extreme value threshold selection and uncertainty with application to ocean storm severity (2015, background): “However, large sample results may provide poor approximations for high thresholds (small number of excesses) and the GP observed information is known to have poor finite-sample properties (Süveges and Davison, 2010).”
Improved threshold diagnostic plots for extreme value analyses (2014, background): “Moreover, in the current context, the observed information is known to have poor finite-sample properties (Süveges and Davison 2010).”