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