High-order Composite Likelihood Inference for Max-Stable Distributions and Processes

TL;DR

This paper investigates the use of high-order composite likelihoods for max-stable processes in multivariate and spatial extremes, aiming to improve inference accuracy while leveraging modern computational capabilities.

Contribution

It demonstrates the feasibility of full likelihood inference for max-stable processes and evaluates the efficiency of high-order composite likelihoods through extensive simulations.

Findings

High-order composite likelihoods can closely approximate full likelihood inference.

Optimal truncation of composite likelihoods enhances inference efficiency.

Recommendations provided for practitioners on likelihood selection and truncation.

Abstract

In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive composite likelihoods constructed from small subsets of data. In this work, we explore the limits of modern state-of-the-art computational facilities to perform full likelihood inference and to efficiently evaluate high-order composite likelihoods. With extensive simulations, we assess the loss of information of composite likelihood estimators with respect to a full likelihood approach for some widely-used multivariate or spatial extreme models, we discuss how to choose composite likelihood truncation to improve the efficiency, and we also provide recommendations for practitioners.