arXiv subjects

Lucien M. Vidagbandji

Publications and source records attributed to Lucien M. Vidagbandji.

3 recordsLinked to original sources

arXiv2026

Existence and consistency of weighted maximum likelihood estimator for extreme quantile regression

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.

stat.ME↗

arXiv2026

Penalized estimation of GEV parameters for extreme quantile regression

Quantile regression (QR) relies on the estimation of conditional quantiles and explores the relationships between independent and dependent variables. At high probability levels, classical QR methods face extrapolation difficulties due to the scarcity of data in the tail of the distribution. Another challenge arises when the number of predictors is large and the quantile function exhibits a complex structure. In this work, we propose an estimation method designed to overcome these challenges. To enhance extrapolation in the tail of the conditional response distribution, we model block maxima using the generalized extreme value (GEV) distribution, where the parameters depend on covariates. To address the second challenge, we adopt an approach based on generalized random forests (grf) to estimate these parameters. Specifically, we maximize a penalized likelihood, weighted by the weights obtained through the grf method. This penalization helps overcome the limitations of the maximum likelihood estimator (MLE) in small samples, while preserving its optimality in large samples. The effectiveness of our method is validated through comparisons with other approaches in simulation studies and an application to U.S. wage data.

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arXiv2025

Generalized random forest for extreme quantile regression

Quantile regression is a statistical method which, unlike classical regression, aims to predict the conditional quantiles. Classical quantile regression methods face difficulties, particularly when the quantile under consideration is extreme, due to the limited number of data available in the tail of the distribution, or when the quantile function is complex. We propose an extreme quantile regression method based on extreme value theory and statistical learning to overcome these difficulties. Following the Block Maxima approach of extreme value theory, we approximate the conditional distribution of block maxima by the generalized extreme value distribution, with covariate-dependent parameters. These parameters are estimated using a method based on generalized random forests. Applications on simulated data show that our proposed method effectively addresses the mentioned quantile regression issues and highlights its performance compared to other quantile regression approaches based on statistical learning methods. We apply our methodology to daily meteorological data from the Fort Collins station in Colorado (USA).

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