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On $$L$$-estimators viewed as $$M$$-estimators. (English) Zbl 0828.62022
Summary: Arithmetical mean and median usually serve as basic examples of $$M$$- estimators. Both of them are $$L$$-estimators. Thus there is a natural question whether there are some other $$L$$-estimators which are $$M$$- estimators as well. We shall show that, with rare exceptions, this is not the case. More precisely, we shall show that the arithmetical mean and empirical quantiles are the only $$L$$-estimators with nonnegative coefficients having a nontrivial $$\psi$$-function.

##### MSC:
 62F10 Point estimation 62G05 Nonparametric estimation
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##### References:
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