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Krylov Sequences as a Tool for Analysing Iterated Regression Algorithms

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  • ANDERS BJÖRKSTRÖM

Abstract

. 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.

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  • Anders Björkström, 2010. "Krylov Sequences as a Tool for Analysing Iterated Regression Algorithms," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 166-175, March.
    • Handle: RePEc:bla:scjsta:v:37:y:2010:i:1:p:166-175
    DOI: 10.1111/j.1467-9469.2009.00668.x
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    References listed on IDEAS

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    1. Neil A. Butler & Michael C. Denham, 2000. "The peculiar shrinkage properties of partial least squares regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 585-593.
    2. O. C. Lingjaerde & Nils Christophersen, 2000. "Shrinkage Structure of Partial Least Squares," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 459-473, September.
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