The Annals of Statistics
- Ann. Statist.
- Volume 9, Number 3 (1981), 578-585.
Tail-Behavior of Location Estimators
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.
Ann. Statist., Volume 9, Number 3 (1981), 578-585.
First available in Project Euclid: 12 April 2007
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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