  The partial least squares procedure was originally developed to estimate the
slope parameter in multivariate parametric models. More recently it has gained
popularity in the functional data literature. There, the partial least squares
estimator of slope is either used to construct linear predictive models, or as
a tool to project the data onto a one-dimensional quantity that is employed for
further statistical analysis. Although the partial least squares approach is
often viewed as an attractive alternative to projections onto the principal
component basis, its properties are less well known than those of the latter,
mainly because of its iterative nature. We develop an explicit formulation of
partial least squares for functional data, which leads to insightful results
and motivates new theory, demonstrating consistency and establishing
convergence rates.
