Tail estimates motivated by extreme value theory
type: Item
instance of: scholarly article
title: Tail estimates motivated by extreme value theory
zbMATH Open document ID: 0555.62035
published in: The Annals of Statistics
publication date: 1984-01-01T00:00:00Z
review text: This paper deals with the problem of estimating the upper tail of a distribution function. The proposed estimator is based on the upper m order statistics from a random sample of size n (m\(\to \infty\), m/n\(\to 0\) as \(n\to \infty)\) and is shown to be consistent for a wide class of distribution functions. Since the empirical mean residual life of the log transformed data and the sample 1-m/n quantile play a key role in the estimator, their joint asymptotic behavior is studied, and rates of convergence of the estimator to the tail are obtained.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 3885123
zbMATH Keywords: tail estimation
zbMATH Keywords: regular variation
zbMATH Keywords: Pareto distribution
zbMATH Keywords: order statistics
zbMATH Keywords: empirical mean residual life
zbMATH Keywords: log transformed data
zbMATH Keywords: rates of convergence
author: Richard A. Davis
author: Sidney I. Resnick
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346804
OpenAlex ID: W2063062722
DOI: 10.1214/AOS/1176346804
description: scientific article; zbMATH DE number 3885123