PARTIAL LEAST-SQUARES - A FIRST-ORDER ANALYSIS

We compare the partial least squares (PLS) and the principal component analysis (PCA), in a general case in which the existence of a true li near regression is not assumed. We prove under mild conditions that PL S and PCA are equivalent, to within a first-order approximation, hence providing a theoretical explanation for empirical findings reported b y other researchers. Next, we assume the existence of a true linear re gression equation and obtain asymptotic formulas for the bias and vari ance of the PLS parameter estimator.