Principal Components Regression with Data-Chosen Components and Related Methods

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Date
2002-05-07
Authors
Hwang, J.
Nettleton, Dan
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Abstract

Multiple regression with correlated explanatory variables is relevant to a broad range of problems in the physical, chemical, and engineering sciences. Chemometricians, in particular, have made heavy use of principal components regression and related procedures for predicting a response variable from a large number of highly correlated variables. In this paper we develop a general theory for selecting principal components that yield estimates of regression coefficients with low mean squared error. Our numerical results suggest that the theory also can be used to improve partial least squares regression estimators and regression estimators based on rotated principal components. Although our work has been motivated by the statistical genetics problem of mapping quantitative trait loci, the results are applicable to any problem where estimation of regression coefficients for correlated explanatory variables is of interest.

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This preprint was published as J.T. Gener Hwang and Dan Nettleton, "Principal Components Regression with Data-Chosen components and Related Methods", Technometrics (2003): 70-79, doi: 10.1198/004017002188618716.

Keywords
Biased regression, Eigenvalues, Mean squared error, Multicollinearity, Partial least squares, Quantitative trait loci, Varimax rotation
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