Fast model selection for robust calibration methods

One of the main issues in principal component regression (PCR) and partial least squares regression (PLSR) is the selection of the number of principal components. To this end, the curve with the root mean squared error of cross-validated prediction (RMSECV) is often described in the literature as a very helpful graphical tool. In this paper, we focus on model selection for robust calibration methods. We first propose a robust RMSECV value and then use it to define a new criterion for the selecting of the optimal number of components. This robust component selection (RCS) statistic combines the goodness-of-fit and the predictive power of the model. As the algorithms to compute these robust PCR and PLSR estimators are more complex and slower than the classical approaches, cross-validation becomes very time consuming. Hence, we propose fast algorithms to compute the robust RMSECV values. We evaluate the developed procedures at several data sets.