Penalized estimation of GEV parameters for extreme quantile regression

TL;DR

This paper introduces a novel penalized GEV-based estimation method for extreme quantile regression that improves tail extrapolation and handles complex predictor structures, validated through simulations and wage data analysis.

Contribution

It combines GEV modeling with penalized likelihood and generalized random forests to enhance extreme quantile estimation in complex, high-dimensional settings.

Findings

Outperforms existing methods in simulation studies.

Effectively models high quantiles in wage data.

Improves tail extrapolation accuracy.

Abstract

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.