Regional extreme value index estimation and a test of homogeneity

Abstract

This paper deals with inference on extremes of heavy tailed distributions. We assume distribution functions F of Pareto-type, i.e. 1-F(x)=x^-1/y L(x) for some γ> 0 and a slowly varying function L : ℝ_+→ℝ_+. Here, the so called extreme value index (EVI) γ is of key importance. In some applications observations from closely related variables are available, with possibly identical EVIγ . If these variables are observed for the same time period, a procedure called BEAR estimator has already been proposed. We modify this approach allowing for different observation periods and pairwise extreme value dependence of the variables. In addition, we present a new test for equality of the extreme value index. As an application, we discuss regional ood frequency analysis, where we want to combine rather short sequences of observations with very different lengths measured at many gauges for joint inference.