Partial Least Squares models under skew-normal and skew-t settings with applications

Abstract

In this work, a new Partial Least Square (PLS) model based on skew-normal (SN) and skew-$t$ (ST) distributions is proposed. This new PLS model may be of interest for applications requiring regression with an asymmetric response variable, heavy-tails, and $R$ support. Furthermore, like PLS, the PLS-SN and PLS-ST address the multicollinearity problem by finding the PLS components that are orthogonal to each other and maximize the covariance between the response variable and PLS components. Simulation studies were conducted to compare the goodness of fit of PLS-SN and PLS-ST models versus the PLS one, using datasets with different sample sizes. Additionally, two real-world data applications were performed, where more favorable information criteria values were found with the PLS-SN and PLS-ST models compared to the PLS one.