On tail index estimation based on multivariate data

A. Dematteo and S. Clémençon

Journal of Nonparametric Statistics, 2016, vol. 28, issue 1, 152-176

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.

Date: 2016
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Citations: View citations in EconPapers (5)

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DOI: 10.1080/10485252.2015.1124105

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