``Asymptotically unbiased'' estimators of the tail index based on external estimation of the second order parameter
type: Item
instance of: scholarly article
title: ``Asymptotically unbiased'' estimators of the tail index based on external estimation of the second order parameter
zbMATH Open document ID: 1037.62044
DOI: 10.1023/A:1020925908039
author: M. Ivette Gomes
author: M. João Martins
published in: Extremes
publication date: 2004-03-16T00:00:00Z
review text: Estimators of the tail index \(\gamma\) of a CDF \(F\) by i.i.d. samples \(X=(X_1,\dots,X_n)\) are investigated in the case were the second order condition \[ \lim_{t\to\infty} (\ln U(tx)-\ln U(t)-\gamma\ln x)/ D\gamma t^\rho =(x^\rho-1)/ \rho \quad \forall x>0 \] holds for \(U(t)=F^{-1}(1-1/t)\). (Recall that \(\gamma=\lim_{t\to\infty}(\ln U(tx)-\ln U(t))/\ln x\)). The authors consider the approximate maximum likelihood estimator \((\widehat\gamma,\widehat D,\widehat\rho)\) for \((\gamma,D,\rho)\) based on \(k\) maximal order statistics of \(X\). Asymptotics of this estimator are investigated. The estimator \(\hat \gamma\) is compared with other estimators for \(\gamma\) via simulations.
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 2059056
zbMATH Keywords: extremes
zbMATH Keywords: semi-parametric estimation
zbMATH Keywords: generalized jackknife statistics
zbMATH Keywords: approximate maximum likelihood estimator
MaRDI profile type: Publication
full work available at URL: a:1020925908039
OpenAlex ID: W114429124
description: scientific article; zbMATH DE number 2059056