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Looking for max-semistability: A new test for the extreme value condition |
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| Authors: | Luí sa Canto e Castro,Maria da Graç a Temido |
| Affiliation: | a CEAUL, DEIO, Faculty of Sciences, University of Lisbon, Portugal b CM-UTAD, Departamento de Matemática, University of Trás-os-Montes and Alto Douro (UTAD), Quinta de Prados, Apartado 1013, 5001-801 Vila Real, Portugal c CMUC, Department of Mathematics, Faculty of Sciences and Technology, University of Coimbra, Portugal |
| Abstract: | To test the extreme value condition, Cramér-Von Mises type tests were recently proposed by Drees et al. (2006) and Dietrich et al. (2002). Hüsler and Li (2006) presented a simulation study on the behavior of these tests and verified that they are not robust for models in the domain of attraction of a max-semistable distribution function. In this work we develop a test statistic that distinguishes quite well distribution functions which belong to a max-stable domain of attraction from those in a max-semistable one. The limit law is deduced and the results from a numerical simulation study are presented. |
| Keywords: | Max-stable models Max-semistable models Hypothesis testing Maximum likelihood estimator Empirical tail quantile function |
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