ABSTRACT

PLS regression has been introduced by H. Wold in the sixties as an algorithm whose aim is to stabilize the least squares estimators. It is now used in a wide range of area, especially chemometrics, econometry, genomics,... Frank and Friedman (1993) showed that PLS regression lead to competitive estimators. However, this method  is sometimes criticized for its lack of statistical justification. In this talk,  we present a new approach based on directional shrinkage factors and we show how PLS regression may be seen as an adaptive version of principal components regression.