On tail index estimation based on multivariate data |
| |
Authors: | A Dematteo S Clémençon |
| |
Institution: | 1. Telecom ParisTech, 46 rue Barrault, 75634 Paris cedex 13, France;2. GazTransport &3. Technigaz (GTT), 1 route de Versailles, 78400 Saint-Rémy-lès-chevreuse, France |
| |
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 |
|
|