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June, 1987 One-Step $L$-Estimators for the Linear Model
A. H. Welsh
Ann. Statist. 15(2): 626-641 (June, 1987). DOI: 10.1214/aos/1176350365


We propose and investigate the asymptotic properties of a class of estimators of the regression parameter in the general linear model. The estimators depend on a preliminary estimate of the regression parameter and the residuals based on it. For the location model, the estimators are linear combinations of the order statistics and the robustness and efficiency properties of this class of estimators carry over to the general linear model. The estimators settle the doubts raised by Bickel (1973) about the feasibility of the construction of a general class of reparametrization invariant estimators of a regression parameter which are linear combinations of order statistics in the location problem.


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A. H. Welsh. "One-Step $L$-Estimators for the Linear Model." Ann. Statist. 15 (2) 626 - 641, June, 1987.


Published: June, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0655.62036
MathSciNet: MR888430
Digital Object Identifier: 10.1214/aos/1176350365

Primary: 62G05
Secondary: 60F05, 62J05

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 2 • June, 1987
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