On tail index estimation based on multivariate data

Abstract

This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, that is, of which Pareto-like marginals share the same tail index. A multivariate central limit theorem for a random vector, whose components correspond to (possibly dependent) Hill estimators of the common tail index α, is established under mild conditions. We introduce the concept of (standard) heavy-tailed random vector of tail index α and show how this limit result can be used in order to build an estimator of α with small asymptotic mean squared error, through a proper convex linear combination of the coordinates. Beyond asymptotic results, simulation experiments illustrating the relevance of the approach promoted are also presented.

Keywords:

• heavy-tail modelling
• multivariate statistics
• tail index estimation
• Hill estimator
• aggregation

AMS Subject Classification:

• 62G32
• 91B30

Conflict of interest disclosure statement

No potential conflict of interest was reported by the authors.