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Asymptotic independence for unimodal densities

Part of:Distribution theoryStochastic processes

Published online by Cambridge University Press:  01 July 2016

Guus Balkema and
Natalia Nolde
Guus Balkema*
Affiliation:
University of Amsterdam
Natalia Nolde*
Affiliation:
ETH Zürich
*
∗ Postal address: Department of Mathematics, University of Amsterdam, Science Park 904, 1098XH Amsterdam, The Netherlands. Email address: a.a.balkema@uva.nl
∗∗ Postal address: Department of Mathematics and RiskLab, ETH Zürich, Raemistrasse 101, 8092 Zürich, Switzerland. Email address: natalia.lysenko@math.ethz.ch
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Abstract

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Asymptotic independence of the components of random vectors is a concept used in many applications. The standard criteria for checking asymptotic independence are given in terms of distribution functions (DFs). DFs are rarely available in an explicit form, especially in the multivariate case. Often we are given the form of the density or, via the shape of the data clouds, we can obtain a good geometric image of the asymptotic shape of the level sets of the density. In this paper we establish a simple sufficient condition for asymptotic independence for light-tailed densities in terms of this asymptotic shape. This condition extends Sibuya's classic result on asymptotic independence for Gaussian densities.

Keywords

Asymptotic independenceblunthomothetic densitylevel setskew normalstar shaped

MSC classification

Primary:60G55: Point processes60G70: Extreme value theory; extremal processes62E20: Asymptotic distribution theory

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 2 , June 2010, pp. 411 - 432
Copyright
Copyright © Applied Probability Trust 2010 

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