On the shrinkage behavior of partial least squares regression

We present a formula for the shrinkage factors of the Partial Least Squares regression estimator and deduce some of their properties, in particular the known fact that some of the factors are >1. We investigate the effect of shrinkage factors for the Mean Squared error of linear estimators and illustrate that we cannot extend the results to nonlinear estimators. In particular, shrinkage factors >1 do not automatically lead to a poorer Mean Squared Error. We investigate empirically the effect of bounding the the absolute value of the Partial Least Squares shrinkage factors by 1.