Extreme Partial Least-Squares regression

Meryem Bousebata (1) , Geoffroy Enjolras (2) , Stéphane Girard (1)

1 STATIFY - Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension
2 CERAG - Centre d'études et de recherches appliquées à la gestion

We propose a new approach, called Extreme-PLS, for dimension reduction in regression and adapted to distribution tails. The objective is to find linear combinations of predictors that best explain the extreme values of the response variable in a non-linear inverse regression model. The asymptotic normality of the Extreme-PLS estimator is established in the single-index framework and under mild assumptions. The performance of the method is assessed on simulated data. A statistical analysis of French farm income data, considering extreme cereal yields, is provided as an illustration.

Mots clés: Extreme-value analysis; Dimension reduction; Non-linear inverse regression; Partial Least Squares.

Domaines: Statistiques [math.ST]

Meryem Bousebata, Geoffroy Enjolras, Stéphane Girard. Extreme Partial Least-Squares regression. 2021. ⟨hal-03165399v1⟩