Abstract
We consider the problem of supervised dimension reduction with a particular focus on extreme values of the target to be explained by a covariate vector . 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.
Funding Statement
Anne Sabourin’s work was partially funded by the ANR projects T-REX and MELODY, and by the chair DSAIDIS from Télécom Paris. Anass Aghbalou was supported by the same chair DSAIDIS.
Acknowledgments
The authors would like to thank three anonymous reviewers and the associate editor for their constructive comments which helped improve the paper.
Citation
Anass Aghbalou. François Portier. Anne Sabourin. Chen Zhou. "Tail inverse regression: Dimension reduction for prediction of extremes." Bernoulli 30 (1) 503 - 533, February 2024. https://doi.org/10.3150/23-BEJ1606