Testing extreme value conditions
type: Item
instance of: scholarly article
title: Testing extreme value conditions
zbMATH Open document ID: 1035.60050
DOI: 10.1023/A:1020934126695
author: Daniel Dietrich
author: Laurens De Haan
author: J. Hüsler
published in: Extremes
publication date: 2004-03-16T00:00:00Z
review text: A modification of the Cramér-von Mises statistics for testing the tail behaviour of i.i.d. sample CDF \(F\) is considered. Its version for nonnegative tail index \(\gamma\) is of the form \[ T_{k,n}=\int \left( {1\over \hat\gamma} (\log X_{n-[kt],n}-\log X_{n-k,n})+\log t \right)^2 t^2\, dt, \] where \(X_{i,n}\) is the \(i\)th order statistics, \(\hat\gamma\) is an estimator for \(\gamma\). It is shown that under proper conditions, \(T_{k,n}\) converges weakly to \[ T=\int_0^1 \left(B(t)+\log t \int_0^1 B(s)/s \,ds\right)^2\,dt, \] where \(B\) is a Brownian bridge, if \(F\) belongs to the domain of max-attraction of the extreme value distribution with the tail index \(\gamma\). Analogous results are obtained for testing \(\gamma\in R\). Results of simulations are presented.
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G32
zbMATH DE Number: 2059060
zbMATH Keywords: Cramer-von Mises test statistics
zbMATH Keywords: asymptotic distribution
zbMATH Keywords: goodness-of-fit
MaRDI profile type: Publication
full work available at URL: a:1020934126695
OpenAlex ID: W4231486800
description: scientific article; zbMATH DE number 2059060