Goodness-of-fit test in extreme value applications

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.