Basis sets for multivariate regression

Estimates of regression coefficients for a multivariate linear model have b een the subject of considerable discussion in the literature. A purpose of this paper is to discuss biased estimators using common basis sets. Estimat ors of focus are least squares, principal component regression, partial lea st squares, ridge regression, generalized ridge regression, continuum regre ssion, and cyclic subspace regression. Variations of these methods are also proposed. It is shown that it is not the common basis set used to span the calibration space or the number of vectors from the common basis set used to form respective calibration models that are important, i.e. a parsimony emphasis. Instead, it is suggested that the size and direction of the calib ration subspace used to form the models is essential, i.e. a harmony consid eration. The approach of the paper is based on representing estimated regre ssion vectors as weighted sums of basis vectors. (C) 2001 Elsevier Science B.V. All rights reserved.