Significance Regression: Robust Regression for Collinear Data

Holcomb, Tyler R. and Morari, Manfred (1993) Significance Regression: Robust Regression for Collinear Data. Technical Report. California Institute of Technology, Pasadena, CA. [CaltechCDSTR:1993.006]

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Abstract

This paper examines robust linear multivariable regression from collinear data. A brief review of M-estimators discusses the strengths of this approach for tolerating outliers and/or perturbations in the error distributions. The review reveals that M-estimation may be unreliable if the data exhibit collinearity. Next, significance regression (SR) is discussed. SR is a successful method for treating collinearity but is not robust. A new significance regression algorithm for the weighted-least-squares error criterion (SR-WLS) is developed. Using the weights computed via M-estimation with the SR-WLS algorithm yields an effective method that robustly mollifies collinearity problems. Numerical examples illustrate the main points.

EPrint Type:	Monograph (Technical Report)
Additional Information:	Partial support this research through the Department of Energy, Office of Basic Energy Sciences is gratefully acknowledged.
Uncontrolled Keywords:	significance regression, biased regression, PLS, multivariable regression, robust regression, collinearity
Subjects:	All Records
ID Code:	71
Deposited By:	Caltech Library System
Deposited On:	28 August 2006
Unique Identifier:	CaltechCDSTR:1993.006
Official Persistent URL:	http://resolver.caltech.edu/CaltechCDSTR:1993.006
Usage Policy:	You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.

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