Influence function analysis for partial least squares with uncorrelated components

Influence theory has been studied extensively in multivariate analysis and detailed results are available for a host of multivariate techniques, including principal components, canonical correlations, and linear discrimination. In this article, the first such results are derived for partial least squares (PLS). In particular, classical perturbation theory is employed to produce theoretical and empirical influence functions for PLS under the constraint of uncorrelated scores. These influence functions are carefully interpreted and then applied to a protein analysis problem.