Asymptotic Minimax Properties of M-estimators of Scale
نویسندگان
چکیده
We ask whether or not the saddlepoint property holds. for robust M-estimation of scale, in gross-errors and Kolmogorov neighbourhoods of certain distributions. This is of interest since the saddlepoint property implies the minimax property that the supremum of the asymptotic variance of an M-estimator is minimized by the maximum likelihood estimator for that member of the distributional class with minimum Fisher information. Our findings are exclusively negative the saddlepoint property fails in all cases investigated. AMS 1980 Subject ClassiJtcations: Primary 62F35; Secondary 62GO5.
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