Krylov Sequences as a Tool for Analysing Iterated Regression Algorithms

We use Krylov sequences to analyse a class of regression methods based on successive identification of latent factors. Some results already proved for partial least squares regression (PLSR) are shown to hold for other methods also. We prove that the well-known peculiar pattern of alternating shrinkage and inflation of the principal components is not unique for PLSR. We also show that for any method in the class under study, the coefficient of determination is always at least as high as for principal components regression with the same number of factors. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.