An offspring of multivariate extreme value theory: the max-characteristic function

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Falk, Michael and Stupfler, Gilles (2017) An offspring of multivariate extreme value theory: the max-characteristic function. Journal of Multivariate Analysis, 154 . pp. 85-95. ISSN 0047-259X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0047259X16301191

Abstract

This paper introduces max-characteristic functions (max-CFs), which are an offspring of multivariate extreme-value theory. A max-CF characterizes the distribution of a random vector in Rd, whose components are nonnegative and have finite expectation. Pointwise convergence of max-CFs is shown to be equivalent to convergence with respect to the Wasserstein metric. The space of max-CFs is not closed in the sense of pointwise convergence. An inversion formula for max-CFs is established.

Item Type:

Article

RIS ID:

https://nottingham-repository.worktribe.com/output/843521

Keywords:

Multivariate extreme-value theory; Max-characteristic function; Wasserstein metric; Convergence

Schools/Departments:

University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences

Identification Number:

https://doi.org/10.1016/j.jmva.2016.10.007

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