arXiv subjects

Alexandre Berred

Publications and source records attributed to Alexandre Berred.

3 recordsLinked to original sources

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.

math.ST↗

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).

stat.ME↗

arXiv2013

Coverage Problem Revisited

Motivated by some problems in genome assembling, we investigate properties of spacings from absolutely continuous distributions. Several results on the asymptotic behavior of the maximal uniform and non-uniform $k$-spacings are presented. Applications of these results to the coverage problem for the prediction stage in genome assembling are also provided.

math.PR↗