The Annals of Statistics

Tail-Behavior of Location Estimators

Jana Jureckova

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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.

Article information

Source
Ann. Statist., Volume 9, Number 3 (1981), 578-585.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345461

Digital Object Identifier
doi:10.1214/aos/1176345461

Mathematical Reviews number (MathSciNet)
MR615433

Zentralblatt MATH identifier
0476.62032

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62G05: Estimation 62G35: Robustness

Keywords
Tails of the distribution sample mean $L$-estimator trimmed mean $M$-estimator median Hodges-Lehmann's estimator

Citation

Jureckova, Jana. Tail-Behavior of Location Estimators. Ann. Statist. 9 (1981), no. 3, 578--585. doi:10.1214/aos/1176345461. https://projecteuclid.org/euclid.aos/1176345461


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