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Significance Regression: A Statistical Approach to Biased Linear Regression and Partial Least Squares

Holcomb, Tyler R. and Hjalmarsson, Hakan and Morari, Manfred (1993) Significance Regression: A Statistical Approach to Biased Linear Regression and Partial Least Squares. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1993.002

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Abstract

This paper first examines the properties of biased regressors that proceed by restricting the search for the optimal regressor to a subspace. These properties suggest features such biased regression methods should incorporate. Motivated by these observations, this work proposes a new formulation for biased regression derived from the principle of statistical significance. This new formulation, significance regression (SR), leads to partial least squares (PLS) under certain model assumptions and to more general methods under various other model kumptions. For models with multiple outputs, SR will be shown to have certain advantages over PLS. Using the new formulation a significance test is advanced for determining the number of directions to be used; for PLS, cross-validation has been the primary method for determining this quantity. The prediction and estimation properties of SR are discussed. A brief numerical example illustrates the relationship between SR and PLS.


Item Type:Report or Paper (Technical Report)
Additional Information:Tyler Holcomb is a recipient of a National Science Foundation Graduate Fellowship. This research was supported by the Caltech Consortium in Chernistry 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. Hikan Hjalmarsson was partially supported by the Swedish Institute and the Blanceflor Boncompagni-Ludovisi Foundation during this work.
Group:Control and Dynamical Systems Technical Reports
Subject Keywords:biased regression, PLS, multivariable regression, significance regression, collinearity
Record Number:CaltechCDSTR:1993.002
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:1993.002
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:28044
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:22 Jul 2006
Last Modified:26 Dec 2012 14:29

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