Partial Least Squares : Afirst - Order Analysis

The main contributions of this paper can be summarized as follows. First, we compare the Partial Least Squares (PLS) and the Principal Component Analysis (PCA), under fairly general conditions. (In particular, the existence of a true linear regression is not assumed.) We prove that PLS and PCA are equivalent, to within a rst-order approximation, hence providing a theoretical explanation for empirical ndings reported by other researchers. Secondly, we assume the existence of a true linear regression equation and obtain an asymptotic formula for the mean-square error (MSE) of the PLS parameter estimator. We use the derived MSE formula in an analytical example to compare the performance achieved by PLS with that of the ordinary LS (OLS).