Abstract
The asymptotic (normal) distribution of an estimator approximates well the central part, but not the tails of its true distribution. Robust estimators, advertised as resistant to heavy-tailed distributions, can be themselves heavy-tailed.
Though asymptotically admissible, many are not finite-sample admissible for any distribution. Hence, before taking a recourse to the asymptotics, we should first analyze finite-sample properties of an estimator, whenever possible.
We illustrate some of the most distinctive differences between the asymptotic and finite-sample properties of robust estimators.