Testing for a multivariate generalized Pareto distribution
It has recently been shown by Rootzén and Tajvidi (Bernoulli, 12:917–930, 2006) that modelling exceedances of a random variable over a high threshold (peaks-over-threshold approach [POT]) can also in the multivariate setup be done rationally only by a multivariate generalized Pareto distribution (GPD). The selection of a proper threshold is, however, a crucial problem. The contribution of this paper is twofold: We develop first a non asymptotic and exact level-α test based on the single-sample t-test, which checks whether multivariate data are actually generated by a multivariate GPD. Secondly, this procedure is utilized for the derivation of a t-test based threshold selection rule in multivariate peaks-over-threshold models. The application to a hydrological data set illustrates this approach.
KeywordsPeaks-over-threshold approach Multivariate extreme value distribution Multivariate generalized Pareto distribution Excess distribution Threshold selection Single-sample t-test
AMS 2000 Subject ClassificationsPrimary—62G32; Secondary—62E15, 62G10, 62H05
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