Noise handling capabilities of multivariate methods

Abstract

The noise handling capabilities of principal component regression (PCR) and partial least squares regression (PLSR) are somewhat disputed issues, especially regarding regressor noise. In an attempt to indicate an answer to the question, this article presents results from Monte Carlo simulations assuming a multivariate mixing problem with spectroscopic data. Comparisons with the best linear unbiased estimator (BLUE) based on Kalman filtering theory are included. The simulations indicate that both PCR and PLSR perform comparatively well even at a considerable regressor noise level. The results are also discussed in relation to estimation of pure spectra for the mixing constituents, i.e. to identification of the data generating system. In this respect solutions to well-posed least squares problems serve as references.