An overview on the shrinkage properties of partial least squares regression

The aim of this paper is twofold. In the first part, we recapitulate the main results regarding the shrinkage properties of partial least squares (PLS) regression. In particular, we give an alternative proof of the shape of the PLS shrinkage factors. It is well known that some of the factors are >1. We discuss in detail the effect of shrinkage factors for the mean squared error of linear estimators and argue that we cannot extend the results to PLS directly, as it is nonlinear. In the second part, we investigate the effect of shrinkage factors empirically. In particular, we point out that experiments on simulated and real world data show that bounding the absolute value of the PLS shrinkage factors by 1 seems to leads to a lower mean squared error.