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Significance Regression: Improved Estimation from Collinear Data for the Measurement Error Model

Holcomb, Tyler R. and Morari, Manfred (1993) Significance Regression: Improved Estimation from Collinear Data for the Measurement Error Model. California Institute of Technology , Pasadena, CA. (Unpublished)

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This paper examines improved regression methods for the linear multivariable measurement error model (MEM) when the data suffers from "collinearity." The difficulty collinearity presents for reliable estinlation is discussed and a systematic procedure, significance regression (SR-MEM), is developed to address collinearity. In addition to mitigating collinearity difficulties SR-MEM produces asymptotically unbiased estimates. The use of ordinary least squares (OLS) for the MEM is examined. For collinear data OLS can improve the mean squared error of estimation over the maximum likelihood (ML) unbiased estimator in a manner analogous to ridge regression (RR). The significance regression method developed for the classical model (SR-classical) can also be used for data with measurement errors. SR-classical is similar SR-MEM and can yield better estimation than the ML estimator for collinear data. Numerical examples illustrate several points.

Item Type:Report or Paper (Technical Report)
Additional Information:The author's thank Håkan Hjalmarsson for his helpful comments concerning asymptotic distributions. This research was partially supported by the Department of Energy, Office of Basic Energy Sciences, and by the Caltech Consortium in Chemistry and Chemical Engineering. Founding members of the Consortium are E. I. du Pont de Nemours and Company, inc., Eastman Kodak Company, Minnesota Mining and Manufacturing Company, and Shell Oil Company Foundation.
Group:Control and Dynamical Systems Technical Reports
Subject Keywords:measurement error models, biased regression, partial least squares, multivariable regression, significance regression, collinearity
Record Number:CaltechCDSTR:1993.004
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Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28047
Deposited By: Imported from CaltechCDSTR
Deposited On:28 Aug 2006
Last Modified:03 Oct 2019 03:28

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