Statistical expansions and locally uniform Fréchet differentiability
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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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Link to Published Version: http://dx.doi.org/10.1017/S1446788700032572
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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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