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

Falk, Michael; Stupfler, Gilles

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.

Citation

Falk, M., & Stupfler, G. (2017). An offspring of multivariate extreme value theory: the max-characteristic function. Journal of Multivariate Analysis, 154, https://doi.org/10.1016/j.jmva.2016.10.007

• Journal Article Type: Article
• Acceptance Date: Oct 22, 2016
• Online Publication Date: Nov 1, 2016
• Publication Date: Feb 28, 2017
• Deposit Date: Jun 27, 2017
• Publicly Available Date: Jun 27, 2017
• Journal: Journal of Multivariate Analysis
• Print ISSN: 0047-259X
• Electronic ISSN: 0047-259X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 154
• DOI: https://doi.org/10.1016/j.jmva.2016.10.007
• Keywords: Multivariate extreme-value theory; Max-characteristic function; Wasserstein metric; Convergence
• Public URL: https://nottingham-repository.worktribe.com/output/843521
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0047259X16301191
• Related Public URLs: https://arxiv.org/abs/1603.02575