Inference for heavy-tailed data with Gaussian dependence

TL;DR

This paper develops methods for consistent estimation of tail indices and Gaussian correlation in multivariate heavy-tailed data with non-identical marginals, supported by theoretical results, simulations, and real data applications.

Contribution

It introduces new estimation techniques for tail indices and Gaussian dependence parameters in complex heavy-tailed models with non-identical marginals.

Findings

Estimates are consistent and asymptotically normal.

Methods perform well in simulations.

Applied successfully to insurance, internet traffic, and network data.

Abstract

We consider a model for multivariate data with heavy-tailed marginal distributions and a Gaussian dependence structure. The different marginals in the model are allowed to have non-identical tail behavior in contrast to most popular modeling paradigms for multivariate heavy-tail analysis. Despite being a practical choice, results on parameter estimation and inference under such models remain limited. In this article, consistent estimates for both marginal tail indices and the Gaussian correlation parameters for such models are provided and asymptotic normality of these estimators are established. The efficacy of the estimation methods are exhibited using extensive simulations and then they are applied to real data sets from insurance claims, internet traffic, and, online networks.