Asymptotic minimax properties of M-estimators of scale

Douglas P. Wiens and K. H. Eden Wu

Statistics & Probability Letters, 1990, vol. 10, issue 5, 363-368

Abstract: 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.

Keywords: Robust; estimation; of; scale; minimum; Fisher; information; for; scale; M-estimates; of; scale; minimax; variance; Kolmogorov; neighbourhood; gross-errors; neighbourhood (search for similar items in EconPapers)
Date: 1990
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