Single-index Extreme-PLS regression

The goal of this communication is to propose a new approach, called Single-index Extreme-PLS, for dimension reduction in regression and adapted to distribution tails. The objective is to find a linear combination of predictors that best explain the extreme values of the response variable in a non-linear inverse regression model. The asymptotic normality of the Single-index Extreme-PLS estimator is established 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.