Statistical expansions and locally uniform Fréchet differentiability
- 1 February 1991
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- Vol. 50 (1) , 88-97
- https://doi.org/10.1017/s1446788700032572
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.Keywords
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