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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.

62F10 Point estimation
62G05 Nonparametric estimation
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