Estimation of the tail exponent of multivariate regular variation
type: Item
instance of: scholarly article
title: Estimation of the tail exponent of multivariate regular variation
zbMATH Open document ID: 1384.62162
author: Moosup Kim
author: Sangyeol Lee
published in: Annals of the Institute of Statistical Mathematics
publication date: 2017-11-16T00:00:00Z
review text: It is well known that the extreme behavior of multivariate observations can be characterized by a spectral measure and a tail exponent. The estimation of this latter quantity is considered here, which is grounded on the fact that every convex combination of a random vector having a multivariate regularly varying tail also has a univariate regularly varying tail with the same exponent (under certain conditions). Specifically, the proposed estimator of the tail exponent is obtained from a weighted average of Hill's estimators obtained for all convex combinations of the given random vector. The asymptotic properties of this estimator together with its finite sample performance are considered. An illustration with financial data concludes the manuscript.
reviewed by: Fabrizio Durante
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62P05
zbMATH DE Number: 6807778
zbMATH Keywords: tail exponent
zbMATH Keywords: multivariate regular variation
zbMATH Keywords: Hill's estimator
zbMATH Keywords: empirical process theory
MaRDI profile type: Publication
full work available at URL: s10463-016-0574-9
OpenAlex ID: W2505705170
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DOI: 10.1007/S10463-016-0574-9
description: scientific article; zbMATH DE number 6807778