Shrinkage structure of partial least squares

Partial least squares regression (PLS) is one method to estimate parameters in a linear model when predictor variables are nearly collinear. One way t o characterize PLS is in terms of the scaling (shrinkage or expansion) alon g each eigenvector of the predictor correlation matrix. This characterizati on is useful in providing a link between PLS and other shrinkage estimators , such as principal components regression (PCR) and ridge regression (RR), thus facilitating a direct comparison of PLS with these methods. This paper gives a detailed analysis of the shrinkage structure of PLS, and several n ew results are presented regarding the nature and extent of shrinkage.