A Proxy-likelihood Estimator for Multivariate Extremes Models with Intractable Likelihoods

2026-09-24

AI Summary

This study addresses the fitting bottleneck in multivariate extreme value models caused by intractable likelihood functions. We propose a surrogate likelihood approach based on tail pairwise dependence. By leveraging the Hüsler-Reiss distribution to establish a one-to-one mapping between dependence parameters and tail pairwise dependence, and integrating regular variation theory with transformed linear extremal time series models, the proposed method enables efficient parameter estimation while supporting likelihood-based model selection. Experimental results demonstrate that our approach yields significantly lower bias than existing methods under weak tail dependence. Furthermore, its application to wildfire risk analysis successfully reveals an intensifying trend in climate-related tail dependence, highlighting the practical utility of the framework for environmental risk assessment.

Abstract

Many multivariate extremes models have intractable likelihoods requiring practitioners to use alternative fitting methods. The tail pairwise dependence is a summary measure of the dependence in the tail of any multivariate regular variation model. We develop an objective function for model fitting that relies on the tail pairwise dependence as the link between our desired model (that does not have a likelihood) and a proxy model (that has a likelihood). We employ the bivariate Hüsler-Reiss distribution as the proxy model and show that there is a one-to-one relationship between the dependence parameter and the tail pairwise dependence value. Our proxy-likelihood estimator is fully developed for the transformed linear extremes time series (TLETS) models of Mhatre and Cooley (2024) and is applied to the wildfire weather data of Wixson and Cooley (2023). Simulations demonstrate that the proxy-likelihood is a competitive TPD estimator, is better at fitting TLETS models than existing methods, and is amenable to likelihood-based model selection techniques. Our estimator has smaller bias when tail dependence is weak than existing estimators reducing the need for bias adjustments. Without these adjustments, we note an increase in the tail dependence in weather-related wildfire risk between past and present climates.

Problem

• Multivariate Extremes
• Intractable Likelihoods
• Model Fitting
• Tail Pairwise Dependence

Innovation

• Proxy-likelihood Estimator
• Multivariate Extremes Models
• Intractable Likelihoods
• Tail Pairwise Dependence
• Hüsler-Reiss Distribution