Bootstrap-based Q̂kh2 for the selection of components and variables in PLS regression

The aim of this paper is to suggest a bootstrap-based method for choosing the number of components in Partial Least Squares Regression (PLSR). Cross-validated Qh2 statistic is used, for which is intended to derive a bootstrap distribution and to perform a hypothesis testing. Monte Carlo approximation is adopted. Applications on both artificial and real data are presented.