“Statistics,” 40 (1), 65-93.

In "Influence analysis for partial least squares with uncorrelated components," William Rayens and co-author Kjell Johnson use classical perturbation theory to derive theoretical and empirical influence functions for the operative eigenstructure constructs associated with partial least squares (PLS). 

Unlike the better known principal components analysis (PCA), explicit endorsement of a constraint set is necessary to meaningfully derive more than one PLS component. This particular manuscript focuses on the most popular constraint set in the chemometrics community, namely uncorrelated component scores.  But this is also the most difficult of the common PLS constraint sets to address, since different PLS components are not indexed by the relative rankings of eigenvalues from a single eigenstructure problem (like PCA), but rather from the lead components from each of a series of different eigenstructure problems.

William Rayens is a professor and director of undergraduate studies in the Department of Statistics in the College of Arts and Sciences at the University of Kentucky.  Rayens received his bachelor’s degree in applied mathematics and religion from Centre College in Kentucky.  He later received a master’s degree in mathematics from the University of North Carolina at Chapel Hill and his doctorate in mathematics from Duke University. Rayens is an associate editor of the “Journal of Chemometrics.” His primary research areas are in bilinear and multilinear structure seeking methodologies.