Asymptotic independence and support detection techniques for heavy-tailed multivariate data

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http://hdl.handle.net/10138/327069

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Lehtomaa , J & Resnick , S 2020 , ' Asymptotic independence and support detection techniques for heavy-tailed multivariate data ' , Insurance: Mathematics and Economics , vol. 93 , pp. 262-277 . https://doi.org/10.1016/j.insmatheco.2020.05.002

Title: Asymptotic independence and support detection techniques for heavy-tailed multivariate data
Author: Lehtomaa, Jaakko; Resnick, Sidney
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2020-07
Language: eng
Number of pages: 16
Belongs to series: Insurance: Mathematics and Economics
ISSN: 0167-6687
URI: http://hdl.handle.net/10138/327069
Abstract: One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently independent. This paper aims to identify asymptotically independent risks by providing tools for describing dependence structures of multiple risks when the individual risks can obtain very large values. The study is performed in the setting of multivariate regular variation. We show how asymptotic independence is connected to properties of the support of the angular measure and present an asymptotically consistent estimator of the support. The estimator generalizes to any dimension N >= 2 and requires no prior knowledge of the support. The validity of the support estimate can be rigorously tested under mild assumptions by an asymptotically normal test statistic. (C) 2020 Elsevier B.V. All rights reserved.
Subject: Multivariate regular variation
Support estimation
Heavy-tailed
Asymptotic independence
Power law
HIDDEN REGULAR VARIATION
POWER-LAW DISTRIBUTIONS
SPECTRAL MEASURE
NONPARAMETRIC-ESTIMATION
DEPENDENCE
EXTREMOGRAM
COEFFICIENT
BEHAVIOR
SET
111 Mathematics
512 Business and Management
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