Tail-behavior of estimators and of their one-step versions

Abstract

The finite-sample breakdown points and finite-sample tail behavior are studied for a class of equivariant estimators in the linear regression model under a fixed design. A lower bound for the tail behavior of an M-estimator is derived, showing how faster are the tails of estimator than the tails of the parent distribution.

The tail behavior of the Newton-Raphson iterations of an estimator is compared with that of the initial estimator.

Keywords

• breakdown point
• equivariant estimator
• tail-behavior