Testing for a multivariate generalized Pareto distribution
- 146 Downloads
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
Unable to display preview. Download preview PDF.
- Coles, S.: An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics, Springer, New York (2001)Google Scholar
- Fougères, A.-L.: Multivariate extremes. In: Finkenstädt, B., Rootzén, H. (eds.) Extreme Values in Finance, Telecommunications, and the Environment, pp. 373–388. Chapman and Hall, Boca Raton (2004)Google Scholar
- Michel, R.: Simulation and estimation in multivariate generalized Pareto Models. Ph.D. thesis, University of Würzburg. Available at http://www.opus-bayern.de/uni-wuerzburg/volltexte/2006/1848/pdf/Simulation_and_Estimation_in_Multivariate_Generalized_Pareto_Models.pdf (2006)
- Pickands III, J.: Multivariate extreme value distributions. In: Proc. 43th Session ISI (Buenos Aires), pp. 859–878. (1981)Google Scholar
- Resnick, S.I.: Extreme values, regular variation, and point processes. In: Applied Prob., vol. 4. Springer, New York (1987)Google Scholar
- Tajvidi, N.: Characterization and some statistical aspects of univariate and multivariate generalised Pareto distributions. Ph.D. thesis, Dept. Math., University of Göteborg (1996)Google Scholar