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December, 1992 Bias Robust Estimation in Orthogonal Regression
Ruben H. Zamar
Ann. Statist. 20(4): 1875-1888 (December, 1992). DOI: 10.1214/aos/1176348893

Abstract

Orthogonal regression $M$-estimates are considered from a bias robust point of view. Their maximum bias over epsilon-contamination neighborhoods is characterized, and maximum bias curves are computed. The most bias robust orthogonal regression $M$-estimate is derived and shown to be a "mode type" estimate; for instance, in the two-dimensional case this estimate can be computed by locating a strip of fixed width covering the maximum number of data points. It will be shown that, although orthogonal regression $M$-estimates with bounded loss function have unbounded influence function, the derivative of their maximum bias curve at zero is finite. Finally, an implicit formula for an upper bound for the breakdown point of all orthogonal regression $M$-estimates is found. The upper bound, which depends on the signal-to-noise ratio, is sharp and attained by the most bias robust estimate.

Citation

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Ruben H. Zamar. "Bias Robust Estimation in Orthogonal Regression." Ann. Statist. 20 (4) 1875 - 1888, December, 1992. https://doi.org/10.1214/aos/1176348893

Information

Published: December, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0784.62051
MathSciNet: MR1193316
Digital Object Identifier: 10.1214/aos/1176348893

Subjects:
Primary: 62J02
Secondary: 62J05

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 4 • December, 1992
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