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 and in the
paper 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
rst step the maximum likelihood approach will be applied to a speci c
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 is included in a Krylov structured design matrix describing the
Linköping, 2010. , 11 p.
MLE; Krylov Design Matrix; PLS; Variance Estimator.