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Trimmed, Bayesian and admissible estimators

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  • Jurecková, Jana
  • Klebanov, Lev B.

Abstract

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

Suggested Citation

  • Jurecková, Jana & Klebanov, Lev B., 1999. "Trimmed, Bayesian and admissible estimators," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 47-51, March.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:1:p:47-51
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    References listed on IDEAS

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    1. Roger W. Koenker & Vasco D'Orey, 1987. "Computing Regression Quantiles," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 383-393, November.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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