Distribution-free prediction regions of multivariate response PLS models with applications to NIR datasets

Abstract

Multi-response partial least squares regression (PLS2) is commonly used in analyzing high-dimensional multi-response data, particularly estimating prediction regions. However, calculating prediction regions by local linearization methods requires the assumption of normality to obtain high coverage level. It has been shown that methods under distribution-free assumption outperform local linearization methods. Therefore, in this work, several new methods are proposed to construct distribution-free prediction regions of PLS2 models. The estimated prediction regions do not rely on trivial assumptions and have relatively lower computational cost. Analyses of simulation and real NIR datasets show that the proposed methods have higher predictive coverage and is more computational effective than local linearization methods.