Efficiency Constrained Bias Robust Estimation of Location
WASHINGTON UNIV SEATTLE DEPT OF STATISTICS
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It has been correctly pointed out by an anonymous referee that the results of this paper amount to a rigorous analysis of the correctness of Hampels heuristic approach in the location setup. Still, one might conjecture by analogy that, in the case of more complicated models, maximizing the efficiency under a constraint on the gross. error-sensitivity is almost the same as putting a constraint on the bias. However, the extension of our technique to more complicated models is by no means straightforward if al all possible and this matter deserves further study. Another interesting issue brought up by an anonymous referee is that if one leaves the realm of M-estimates of location, there is not necessarily a pay-off between bias-robustness and efficiency at the central Gaussian model.
- Statistics and Probability