Looking for Max-Semistability: a New Test for the Extreme Value Condition

Journal of Statistical Planning and Inference, 141(9) (2011), 3005-3020
http://dx.doi.org/10.1016/j.jspi.2011.03.020

To test the extreme value condition, Cramer-Von Mises type tests were recently proposed by Drees et al. (2006) and Dietrich et al. (2002). Husler 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. (C) 2011 Elsevier B.V. All rights reserved.