Semi-parametric approach to the Hasofer–Wang and Greenwood statistics in extremes

Abstract

This paper deals with the semi-parametric approach to the problem of statistical choice of extreme domains of attraction. Relying on concepts of regular variation theory, it investigates the asymptotic properties of Hasofer and Wang’s test statistic based on the k upper extremes taken from a sample of size n, when k behaves as an intermediate sequence kn rather than remaining fixed while the sample size increases. In the process a Greenwood type test statistic is proposed which turns out to be useful in discriminating heavy-tailed distributions. The finite sample behavior of both testing procedures is evaluated in the light of a simulation study. The testing procedures are then applied to three real data sets.