A0165
Title: Generalized random forest for extreme quantile regression
Authors: Mahutin Lucien Vidagbandji - LMAH-University of Le Havre Normandy (France) [presenting]
Alexandre Berred - University of Le Havre Normandy- LMAH (France)
Cyrille Bertelle - LITIS-University of Le Havre Normandy (France)
Laurent Amanton - LITIS-University of Le Havre Normandy (France)
Abstract: Quantile regression is a commonly used statistical method in regression analysis. In contrast to classical regression, which centers on predicting the conditional mean of a dependent variable based on independent variables, quantile regression aims to predict conditional quantiles. Specifically, if $Y \in \mathcal{Y} \subset \mathbb{R}$ represents a random variable describing a risk factor dependent on a set of covariates represented by the random vector $X \in \mathcal{X} \subset \mathbb{R}^p$, the goal is to estimate the conditional extreme quantile given by: $\mathcal{Q}_{\tau}(x) = \inf \{ y : F_{Y|X=x}(y) \geq \tau \}$ with $\tau \in [0,1]$. Classical quantile regression methods face challenges, especially when the quantile of interest 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 challenges. Following the Block Maxima (BM) approach of extreme value theory, we approximate the conditional distribution of BM by the generalized extreme value distribution, with parameters depending on covariates. To estimate these parameters, we employ a method based on generalized random forests. Simulated data applications highlight our method's performance compared to other statistical learning-based quantile regression approaches.
