Trimmed, Bayesian and admissible estimators
The authors proved in [5] that the robust M- and L-estimators of location, which are independent of the extreme order statistics of the sample, cannot be admissible with respect to L1 risk in the class of translation equivariant estimators. This result is now extended in two respects: (i) We show that these estimators cannot be even Bayesian, under some regularity conditions, with respect to a strictly convex and continuously differentiable loss function; (ii) moreover, we extend the result to the linear regression model and show the inadmissibility of regression equivariant estimators, trimming-off the observations with nonpositive [nonnegative] residuals with respect to [alpha]1- [[alpha]2]-regression quantiles, respectively, for some 0<[alpha]1<[alpha]2<1. This among others implies the inadmissibility of the trimmed LSE of Koenker and Bassett [Koenker, R., Bassett, G., 1978. Regression quantiles. Econometrica 46, 466-476.] with respect to Lp (p[greater-or-equal, slanted]2) or to other smooth convex loss functions.
Year of publication: |
1999
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Authors: | Jurecková, Jana ; Klebanov, Lev B. |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 42.1999, 1, p. 47-51
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Publisher: |
Elsevier |
Subject: | Admissibility Bayesian estimators Trimmed estimators |
Saved in:
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