Tail Inverse Regression: dimension reduction for prediction of extremes

Anass Aghbalou (1, 2) , François Portier (3) , Anne Sabourin (4) , Chen Zhou (5, 6)

1 IDS - Département Images, Données, Signal
2 S2A - Signal, Statistique et Apprentissage
3 ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz]
4 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
5 Erasmus University Rotterdam
6 Tinbergen Institute, Rotterdam

We consider the problem of supervised dimension reduction with a particular focus on extreme values of the target Y ∈ R to be explained by a covariate vector X ∈ R p. The general purpose is to define and estimate a projection on a lower dimensional subspace of the covariate space which is sufficient for predicting exceedances of the target above high thresholds. We propose an original definition of Tail Conditional Independence which matches this purpose. Inspired by Sliced Inverse Regression (SIR) methods, we develop a novel framework (TIREX, Tail Inverse Regression for EXtreme response) in order to estimate an extreme sufficient dimension reduction (SDR) space of potentially smaller dimension than that of a classical SDR space.We prove the weak convergence of tail empirical processes involved in the estimation procedure and we illustrate the relevance of the proposed approach on simulated and real world data.

Keywords: MSC2020 subject classifications: Primary 62G32 62H25; secondary 62G08 62G30; Dimension reduction; Empirical processes; Extreme events; Inverse regression; Supervised learning

Domains: Mathematics [math]; Statistics [stat]

Anass Aghbalou, François Portier, Anne Sabourin, Chen Zhou. Tail Inverse Regression: dimension reduction for prediction of extremes. 2023. ⟨hal-04032206⟩