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March, 1986 Maximum Asymptotic Variances of Trimmed Means Under Asymmetric Contamination
John R. Collins
Ann. Statist. 14(1): 348-354 (March, 1986). DOI: 10.1214/aos/1176349861


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 $F = (1 - \varepsilon)F_0 + \varepsilon G$, where $F_0$ is a known distribution symmetric about $0, \varepsilon$ is 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.


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John R. Collins. "Maximum Asymptotic Variances of Trimmed Means Under Asymmetric Contamination." Ann. Statist. 14 (1) 348 - 354, March, 1986.


Published: March, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0587.62076
MathSciNet: MR829574
Digital Object Identifier: 10.1214/aos/1176349861

Primary: 62F35
Secondary: 62F12

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 1 • March, 1986
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