J Austral Math Soc Ser A 50 pp88--97, 1991.

Statistical Expansions and Locally Uniform Fréchet Differentiability

T. Bednarski, B. R. Clarke and W. Kolkiewicz

(Received 23 June 1989; revised 9 NOvember 1989)

Abstract

Estimators which have locally uniform expansions are shown in this paper to be asymptotically equivalent to M-estimators. The M-functionals corresponding to these M-estimators are seen to be locally uniformly Fréchet differentiable. Other conditions for M-functionals to be locally uniformly Fréchet differentiable are given. An example of a commonly used estimate which is robust against outliers is given to illustrate that the locally uniform expansion need not be valid.

1980 AMS Subject Classification (1985 Revision): primary 62E20; secondary 62G35

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Authors

T. Bednarski: Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland.
B. R. Clarke: Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland.
W. Kolkiewicz: Murdoch University, Murdoch, WA 6150, Australia.

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Last Modified: Mon Feb 3 9:46:09 2003