Tail Inverse Regression: dimension reduction for prediction of extremes - Laboratoire Traitement et Communication de l'Information Access content directly
Preprints, Working Papers, ... Year : 2023

Tail Inverse Regression: dimension reduction for prediction of extremes

Abstract

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.
Fichier principal
Vignette du fichier
main_tirex_arxiv_v2.pdf (1.01 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04032206 , version 1 (16-03-2023)

Identifiers

Cite

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

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More