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Statistical expansions and locally uniform Fréchet differentiability

Bednarski, T., Clarke, B.R. and Kolkiewicz, W. (1991) Statistical expansions and locally uniform Fréchet differentiability. Journal of the Australian Mathematical Society (Series A), 50 (01). pp. 88-97.

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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 estimator which is robust against outliers is given to illustrate that the locally uniform expansion need not be valid.

Publication Type: Journal Article
Murdoch Affiliation: School of Chemical and Mathematical Science
Publisher: Cambridge University Press
Copyright: © 1991 Australian Mathematical Society
URI: http://researchrepository.murdoch.edu.au/id/eprint/4803
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