Maximum asymptotic variances of trimmed means under asymmetric contamination
type: Item
instance of: scholarly article
title: Maximum asymptotic variances of trimmed means under asymmetric contamination
zbMATH Open document ID: 0587.62076
author: John R. Collins
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: We consider the following problem arising in robust estimation theory: Find the maximum asymptotic variance of a trimmed mean used to estimate an unknown location parameter when the error distribution is subject to asymmetric contamination. The model for the error distribution is \(F=(1-\epsilon)F_ 0+\epsilon G,\) where \(F_ 0\) is a known distribution symmetric about 0, \(\epsilon\) is a fixed proportion of contamination, and G is an unknown and possibly asymmetric distribution. We prove, under the assumption that \(F_ 0\) has a symmetric unimodal density function \(f_ 0\), that the maximal asymptotic variance is obtained when G places mass 1 at either \(+\infty\) or -\(\infty\). The key idea of the proof is first to maximize the asymptotic variance subject to the side conditions \(F(a)=\alpha\) and \(F(b)=1-\alpha\) when a and b are given.
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 3942761
zbMATH Keywords: robust estimation
zbMATH Keywords: maximum asymptotic variance of a trimmed mean
zbMATH Keywords: location
zbMATH Keywords: asymmetric contamination
zbMATH Keywords: symmetric unimodal density
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349861
OpenAlex ID: W2095582514
DOI: 10.1214/AOS/1176349861
description: scientific article; zbMATH DE number 3942761