A note on robustness of the β-trimmed mean

Clarke, B.R., Gamble, D.K. and Bednarski, T. (2000) A note on robustness of the β-trimmed mean. Australian & New Zealand Journal of Statistics, 42 (1). pp. 113-117.

Abstract

Qualitative robustness of the β-trimmed mean has already been observed in terms of relative efficiency and weak continuity of that estimator in neighbourhoods of the exponential distribution. Two more robustness considerations are given here in favour of the β-trimmed mean: the statistical functional representing this estimator is Fréchet differentiable; and it is a special case of the trimmed likelihood estimator. Further, simulations suggest that a fixed proportion of trimming is preferable to adaptive estimation in this case.