Max-Linear Tail Regression

TL;DR

This paper introduces a max-linear tail regression model tailored for extreme covariate values, along with a novel M-estimator based on extreme value theory, demonstrating superior performance over traditional methods through simulations and real data case studies.

Contribution

The paper presents a new max-linear tail regression model and an M-estimator for extreme value relationships, with theoretical guarantees and practical validation.

Findings

Estimator outperforms conditional least squares in simulations

Model effectively captures extreme covariate effects

Validated on financial and rainfall data

Abstract

The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically designed to capture such extreme relationships. To estimate the regression coefficients within this framework, we propose a novel M-estimator based on extreme value theory. The consistency and asymptotic normality of our proposed estimator are rigorously established under mild conditions. Simulation results demonstrate that our estimation method outperforms the conditional least squares approach. We validate the practical applicability of our model through two case studies: one using financial data and the other using rainfall data.