Convergence rates for the moments of extremes
type: Item
instance of: scholarly article
zbMATH Open document ID: 1275.62049
DOI: 10.4134/BKMS.2012.49.3.495
published in: Bulletin of the Korean Mathematical Society
publication date: 2012-06-08T00:00:00Z
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 6044474
zbMATH Keywords: domain of attraction
zbMATH Keywords: extreme value distributions
zbMATH Keywords: maximum
zbMATH Keywords: second order regular variation
zbMATH Keywords: second order von Mises condition
author: Zuoxiang Peng
author: Saralees Nadarajah
MaRDI profile type: Publication
full work available at URL: bkms.2012.49.3.495
OpenAlex ID: W1997008837
title: Convergence rates for the moments of extremes
review text: Let \(X_1,\dots,X_n\) be independent copies of a random variable \(X\) such that NEWLINE\[NEWLINEM_n:=(\max_{1\leq i\leq n}X_i-b_n)/a_nNEWLINE\]NEWLINE converges in distribution with some norming sequences \(a_n>0\), \(b_n\in\mathbb R\), to a random variable \(\xi\), which follows an extreme value distribution. It is known that under appropriate conditions including \(E(|X|^k)<\infty\), one has \(\lim_{n\to\infty}E(M_n^k)=E(\xi^k)\) for an integer \(k>0\). The paper provides second order regularity conditions on the distribution function of \(X\), such that \((E(M_n^k)-E(\xi^k))/A(n)\) has a non degenerate limit as \(n\) tends to infinity, where \(A(\cdot)\) is an appropriate norming function.
reviewed by: Michael Falk
description: scientific article; zbMATH DE number 6044474