2014/11/02 by Mélanie Blazère, Fabrice Gamboa, Blazère, Mélanie +3
Chemistry · Computer Science · Mathematics · #Advanced Statistical Methods and Models #Blind Source Separation Techniques #FOS: Mathematics #Spectroscopy and Chemometric Analyses #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1411.0229
openalex publication_date 2014/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.