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September 2016 One-component regular variation and graphical modeling of extremes
Adrien Hitz, Robin Evans
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J. Appl. Probab. 53(3): 733-746 (September 2016).

Abstract

The problem of inferring the distribution of a random vector given that its norm is large requires modeling a homogeneous limiting density. We suggest an approach based on graphical models which is suitable for high-dimensional vectors. We introduce the notion of one-component regular variation to describe a function that is regularly varying in its first component. We extend the representation and Karamata's theorem to one-component regularly varying functions, probability distributions and densities, and explain why these results are fundamental in multivariate extreme-value theory. We then generalize the Hammersley–Clifford theorem to relate asymptotic conditional independence to a factorization of the limiting density, and use it to model multivariate tails.

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Adrien Hitz. Robin Evans. "One-component regular variation and graphical modeling of extremes." J. Appl. Probab. 53 (3) 733 - 746, September 2016.

Information

Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1353.60036
MathSciNet: MR3570091

Subjects:
Primary: 60F99
Secondary: 60E05 , 60G70 , 62H99

Keywords: Graphical model , homogeneous distribution , Karamata's theorem , multivariate exceedances over threshold , regular variation

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 3 • September 2016
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