Existence and consistency of weighted maximum likelihood estimator for extreme quantile regression
Abstract
Estimating extreme conditional quantiles faces two major challenges: understanding complex nonlinear relationships between variables and accurately extrapolating into the tails of the distribution, where data are sparse. To address both issues, we introduce a novel approach that combines the theoretical framework of block maxima with the predictive power of generalized random forests. The conditional distribution of maxima is modeled by a generalized extreme value (GEV) distribution whose parameters depend on the covariates and are estimated via a weighted maximum likelihood procedure, with weights derived from generalized random forests to capture complex high-dimensional structures. The conditional quantile estimator follows from the inversion of the estimated GEV distribution function. We establish theoretical results ensuring the existence and consistency of the proposed weighted maximum likelihood estimator. The method provides a robust and flexible framework for extreme quantile regression. The performance of the proposed approach is illustrated using simulated data, as well as an application to financial portfolio losses from stocks listed on the NYSE, AMEX, and NASDAQ.
Related
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BibTeX
@misc{vidagbandji2026existence,
title = {{Existence and consistency of weighted maximum likelihood estimator for extreme quantile regression}},
author = {Lucien M. Vidagbandji and Alexandre Berred and Cyrille Bertelle and Laurent Amanton},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07344},
eprint = {2610.07344},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05782652v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Existence and consistency of weighted maximum likelihood estimator for extreme quantile regression
AU - Lucien M. Vidagbandji
AU - Alexandre Berred
AU - Cyrille Bertelle
AU - Laurent Amanton
PY - 2026
DA - 2026/10/05
PB - HAL
DO - 10.48550/arxiv.2610.07344
UR - https://hal.science/hal-05782652v1
AB - Estimating extreme conditional quantiles faces two major challenges: understanding complex nonlinear relationships between variables and accurately extrapolating into the tails of the distribution, where data are sparse. To address both issues, we introduce a novel approach that combines the theoretical framework of block maxima with the predictive power of generalized random forests. The conditional distribution of maxima is modeled by a generalized extreme value (GEV) distribution whose parameters depend on the covariates and are estimated via a weighted maximum likelihood procedure, with weights derived from generalized random forests to capture complex high-dimensional structures. The conditional quantile estimator follows from the inversion of the estimated GEV distribution function. We establish theoretical results ensuring the existence and consistency of the proposed weighted maximum likelihood estimator. The method provides a robust and flexible framework for extreme quantile regression. The performance of the proposed approach is illustrated using simulated data, as well as an application to financial portfolio losses from stocks listed on the NYSE, AMEX, and NASDAQ.
ER -