ASYMPTOTIC MINIMAX PROPERTIES OF L-ESTIMATORS OF SCALE

This paper asks whether or not the efficient L-estimator of scale corresponding to the least informative distribution in ε-contamination and Kol-mogorov neighbourhoods of certain distributions possesses the saddlepoint property. This is of interest since the saddlepoint property implies the mini-max property, namely, that the supremum of the relative asymptotic variance of an L-estimator is minimized by the efficient estimator corresponding to that member of the distributional class with minimum Fisher information for scale. Our findings are negative in all cases investigated.