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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 linear regression is not assumed. We prove under mild conditions that PLS and PCA are equivalent, to within a first‐order approximation, hence providing a theoretical explanation for empirical findings reported by other researchers. Next, we assume the existence of a true linear regression equation and obtain asymptotic formulas for the bias and variance of the PLS parameter estimator