Regression context for the Partial Least Squares framework for Extreme values. Estimations of the Shrinkage for Extreme Partial Least-Squares (SEPaLS) estimators, an adaptation of the original Partial Least Squares (PLS) method tailored to the extreme-value framework. The SEPaLS project is a joint work by Stephane Girard, Hadrien Lorenzo and Julyan Arbel. R code to replicate the results of the paper is available at <https://github.com/hlorenzo/SEPaLS_simus>. Extremes within PLS was already studied by one of the authors, see M Bousebeta, G Enjolras, S Girard (2023) <doi:10.1016/j.jmva.2022.105101>.