Testing conditions and estimating parameters in extreme value theory: Application to environmental data

Extreme Value Theory has been asserting itself as one of the most important statistical theories for the applied sciences providing a solid theoretical basis for deriving statistical models describing extreme or even rare events. The efficiency of the inference and estimation procedures depends on the tail shape of the distribution underlying the data. In this work we will present a review of tests for assessing extreme value conditions and for the choice of the extreme value domain. Motivated by two real environmental problems we will apply those tests showing the need of performing such tests for choosing the most appropriate parameter estimation methods.