  In this paper we propose a new approach to study the properties of the
Partial Least Squares (PLS) estimator. This approach relies on the link between
PLS and discrete orthogonal polynomials. Indeed many important PLS objects can
be expressed in terms of some specific discrete orthogonal polynomials, called
the residual polynomials. Based on the explicit analytical expression we have
stated for these polynomials in terms of signal and noise, we provide a new
framework for the study of PLS. Furthermore, we show that this new approach
allows to simplify and retreive independent proofs of many classical results
(proved earlier by different authors using various approaches and tools). This
general and unifying approach also sheds new light on PLS and helps to gain
insight on its properties.
