a1 Institute of Mathematics Polish Academy of Sciences Warsaw, Poland
a2 Institute of Mathematics Polish Academy of Sciences Warsaw, Poland
a3 Murdoch University Murdoch, WA 6150, Australia
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.
(Received June 23 1989)
(Revised November 09 1989)
1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision)
Keywords and phrases