Generalized random forest for extreme quantile regression

TL;DR

This paper introduces a novel extreme quantile regression method combining extreme value theory with generalized random forests, effectively addressing challenges in predicting rare, extreme quantiles in complex distributions.

Contribution

It develops a new approach that models conditional extreme quantiles using generalized extreme value distributions estimated via random forests, improving accuracy for tail predictions.

Findings

Effective in modeling extreme quantiles in simulated data

Outperforms existing quantile regression methods in tail estimation

Successfully applied to meteorological data for extreme weather analysis

Abstract

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).