Goodness-of-fit test in extreme value applications

Abstract

Inference for extreme values based on the generalized extreme value distributions has become a standard practice in the last decades. We summarize the available tests for checking the conditions for these procedures. Besides the well-known Kolmogorov-Smirnov and Anderson-Darling tests two new procedures are also presented. We give the critical values to the methods and compare their properties for simulated as well as real hydrological data. Similar results are given for the case, when the modelling is based on the excess distribution (generalized Pareto). Finally a likelihood ratio test is given for the expected shortfall which is an important risk measure for financial data.