Robust iteratively reweighted SIMPLS

Partial least squares regression is a very powerful multivariate regression technique to model multicollinear data or situation where the number of explanatory variables is larger than the sample size. Two algorithms, namely, Non-linear Iterative Partial Least Squares (NIPALS) and Straightforward implementation of a statistically inspired modification of the partial least squares (SIMPLS) are very popular to solve a partial least squares regression problem. Both procedures, however, are very sensitive to the presence of outliers, and this might lead to very poor fit for the bulk of the data. A robust procedure, which is a modification of the SIMPLS algorithm, is introduced and its performance is illustrated by an extensive Monte Carlo simulation and 2 applications to real data sets. The new procedure is compared with the most recent proposals in literature demonstrating a better robust performance. Partial least squares is a very powerful multivariate regression technique to model multicollinear data or situation where the number of explanatory variables is larger than the sample size. NIPALS and SIMPLS are two very popular algorithm for the PLS problem, however they are sensitive to outliers, and this leads to poor fit for the bulk of the data. A robust procedure RWSIMPLS is introduced and its performance illustrated by a Monte Carlo simulation and 2 applications to real data sets.