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February 2001 Maximum Bias Curves for Robust Regression with Non-elliptical Regressors
José Berrendero, Ruben H. Zamar
Ann. Statist. 29(1): 224-251 (February 2001). DOI: 10.1214/aos/996986507

Abstract

Maximum bias curves for some regression estimates were previously derived assuming that (i) the intercept term is known and/or (ii) the regressors have an elliptical distribution. We present a single method to obtain the maximum bias curves for a large class of regression estimates. Our results are derived under very mild conditions and, in particular, do not require the restrictive assumptions (i) and (ii) above. Using these results it is shown that the maximum bias curves heavily depend on the shape of the regressors' distribution which we call the x-configuration. Despite this big effect, the relative performance of different estimates remains unchanged under different x-configurations. We also explore the links between maxbias curves and bias bounds. Finally, we compare the robustness properties of some estimates for the intercept parameter.

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José Berrendero. Ruben H. Zamar. "Maximum Bias Curves for Robust Regression with Non-elliptical Regressors." Ann. Statist. 29 (1) 224 - 251, February 2001. https://doi.org/10.1214/aos/996986507

Information

Published: February 2001
First available in Project Euclid: 5 August 2001

zbMATH: 1029.62028
MathSciNet: MR1833964
Digital Object Identifier: 10.1214/aos/996986507

Subjects:
Primary: 62F35

Keywords: \tao-estimates , maxbias curve , R-estimates , robust regression , S-estimates

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 1 • February 2001
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