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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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|
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