Trimmed, Bayesian and admissible estimators

✍ Scribed by Jana Jurećková; Lev B. Klebanov

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 88 KB
• Volume: 42
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(98)00187-4

✦ Synopsis

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 di erentiable loss function; (ii) moreover, we extend the result to the linear regression model and show the inadmissibility of regression equivariant estimators, trimming-o the observations with nonpositive [nonnegative] residuals with respect to 1-[ 2]-regression quantiles, respectively, for some 0 ¡ 1 ¡ 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¿2) or to other smooth convex loss functions.