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Statistical expansions and locally uniform Fréchet differentiability

Bednarski, T., Clarke, B.R.ORCID: 0000-0003-1419-0768 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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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.

Item Type: Journal Article
Murdoch Affiliation: School of Chemical and Mathematical Science
Publisher: Cambridge University Press
Copyright: © 1991 Australian Mathematical Society
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