Rank-based Estimation under Asymptotic Dependence and Independence, with Applications to Spatial Extremes

TL;DR

This paper develops rank-based M-estimators for multivariate extreme value models that work under both asymptotic dependence and independence, with applications to spatial extremes, providing theoretical guarantees.

Contribution

It introduces a unified non-parametric estimation method that handles both dependence regimes without prior knowledge, with proven asymptotic normality and spatial applications.

Findings

Estimators are asymptotically normal under weak conditions.

Method applies to spatial tail models with theoretical validation.

Works seamlessly under asymptotic dependence and independence.

Abstract

Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the variables is of the same order as observing a large value in all variables simultaneously. However, there is growing evidence that asymptotic independence is equally important in real world applications. Available statistical methodology in the latter setting is scarce and not well understood theoretically. We revisit non-parametric estimation and introduce rank-based M-estimators for parametric models that simultaneously work under asymptotic dependence and asymptotic independence, without requiring prior knowledge on which of the two regimes applies. Asymptotic normality of the proposed estimators is established under weak regularity conditions. We further show how bivariate estimators can be leveraged to obtain parametric estimators in spatial tail models, and again provide a thorough theoretical justification for our approach.