EVIboost for the Estimation of Extreme Value Index under Heterogeneous Extremes

TL;DR

This paper introduces EVIboost, a gradient boosting algorithm designed to accurately estimate the extreme value index in heterogeneous tail distributions, capturing complex dependencies and dynamics in real-world data.

Contribution

The paper presents a novel gradient boosting method for functional extreme value index estimation that accounts for heterogeneity and complex tail-covariate relationships.

Findings

The algorithm achieves high prediction accuracy in simulations.

It reveals state-dependent and time-varying tail behaviors in financial data.

Extensive simulations validate the method's effectiveness.

Abstract

Modeling heterogeneity on heavy-tailed distributions under a regression framework is challenging, and classical statistical methodologies usually place conditions on the distribution models to facilitate the learning procedure. However, these conditions are likely to overlook the complex dependence structure between the heaviness of tails and the covariates. Moreover, data sparsity on tail regions also makes the inference method less stable, leading to largely biased estimates for extreme-related quantities. This paper proposes a gradient boosting algorithm to estimate a functional extreme value index with heterogeneous extremes. Our proposed algorithm is a data-driven procedure that captures complex and dynamic structures in tail distributions. We also conduct extensive simulation studies to show the prediction accuracy of the proposed algorithm. In addition, we apply our method to a real-world data set to illustrate the state-dependent and time-varying properties of heavy-tail phenomena in the financial industry.