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May, 1981 Tail-Behavior of Location Estimators
Jana Jureckova
Ann. Statist. 9(3): 578-585 (May, 1981). DOI: 10.1214/aos/1176345461

Abstract

Let $X_1, \cdots, X_n$ be a sample from a population with density $f(x - \theta)$ such that $f$ is symmetric and positive. It is proved that the tails of the distribution of a translation-invariant estimator of $\theta$ tend to 0 at most $n$ times faster than the tails of the basic distribution. The sample mean is shown to be good in this sense for exponentially-tailed distributions while it becomes poor if there is contamination by a heavy-tailed distribution. The rates of convergence of the tails of robust estimators are shown to be bounded away from the lower as well as from the upper bound.

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Jana Jureckova. "Tail-Behavior of Location Estimators." Ann. Statist. 9 (3) 578 - 585, May, 1981. https://doi.org/10.1214/aos/1176345461

Information

Published: May, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0476.62032
MathSciNet: MR615433
Digital Object Identifier: 10.1214/aos/1176345461

Subjects:
Primary: 62F10
Secondary: 62G05, 62G35

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 3 • May, 1981
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