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Statistical expansions and locally uniform Fréchet differentiability

Published online by Cambridge University Press:  09 April 2009

T. Bednarski
Affiliation:
Institute of MathematicsPolish Academy of Sciences Warsaw, Poland
B. R. Clarke
Affiliation:
Institute of MathematicsPolish Academy of Sciences Warsaw, Poland
W. Kolkiewicz
Affiliation:
Murdoch UniversityMurdoch, WA 6150, Australia
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1991

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