Tail dimension reduction for extreme quantile estimation

Abstract

In a regression context where a response variable Y ∈ ℝ is recorded with a covariate X ∈ ℝ p , two situations can occur simultaneously: (a) we are interested in the tail of the conditional distribution and not on the central part of the distribution and (b) the number p of regressors is large. To our knowledge, these two situations have only been considered separately in the literature. The aim of this paper is to propose a new dimension reduction approach adapted to the tail of the distribution in order to propose an efficient conditional extreme quantile estimator when the dimension p is large. The results are illustrated on simulated data and on a real dataset.