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December, 1993 Aspects of Robust Linear Regression
P. L. Davies
Ann. Statist. 21(4): 1843-1899 (December, 1993). DOI: 10.1214/aos/1176349401


Section 1 of the paper contains a general discussion of robustness. In Section 2 the influence function of the Hampel-Rousseeuw least median of squares estimator is derived. Linearly invariant weak metrics are constructed in Section 3. It is shown in Section 4 that $S$-estimators satisfy an exact Holder condition of order 1/2 at models with normal errors. In Section 5 the breakdown points of the Hampel-Krasker dispersion and regression functionals are shown to be 0. The exact breakdown point of the Krasker-Welsch dispersion functional is obtained as well as bounds for the corresponding regression functional. Section 6 contains the construction of a linearly equivariant, high breakdown and locally Lipschitz dispersion functional for any design distribution. In Section 7 it is shown that there is no inherent contradiction between efficiency and a high breakdown point. Section 8 contains a linearly equivariant, high breakdown regression functional which is Lipschitz continuous at models with normal errors.


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P. L. Davies. "Aspects of Robust Linear Regression." Ann. Statist. 21 (4) 1843 - 1899, December, 1993.


Published: December, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0797.62026
MathSciNet: MR1245772
Digital Object Identifier: 10.1214/aos/1176349401

Primary: 62F35
Secondary: 62J05

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 4 • December, 1993
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