Abstract

Univariate partial least squares regression (PLS1) is a method of modeling relationships between a response variable and explanatory variables, especially when the explanatory variables are almost collinear. The purpose is to predict a future response observation, although in many applications there is an interest to understand the contributions of each explanatory variable. It is an algorithmic approach. In this article, we are going to use the algorithm presented by Helland (1988). The population PLS predictor is linked to a linear model including a Krylov design matrix and a two-step estimation procedure. For the first step, the maximum likelihood approach is applied to a specific multivariate linear model, generating tools for evaluating the information in the explanatory variables. It is shown that explicit maximum likelihood estimators of the dispersion matrix can be obtained where the dispersion matrix, besides representing the variation in the error, also includes the Krylov structured design matrix describing the mean.

Keywords

Krylov design; Krylov sequence; Krylov space; Maximum likelihood estimators; PLS; Variance estimator

Published in

Communications in Statistics - Theory and Methods
2012, Volume: 41, number: 13-14, pages: 2503-2511

SLU Authors

• Li, Ying

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    

• von Rosen, Dietrich

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    

UKÄ Subject classification

Probability Theory and Statistics


Publication identifier

DOI: https://doi.org/10.1080/03610926.2011.607531

Permanent link to this page (URI)

https://res.slu.se/id/publ/50343