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Extremal measures maximizing functionals based on simplicial volumes

Pronzato, Luc, Wynn, Henry P. and Zhigljavsky, Anatoly ORCID: 2016. Extremal measures maximizing functionals based on simplicial volumes. Statistical Papers 57 , pp. 1059-1075. 10.1007/s00362-016-0767-6

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We consider functionals measuring the dispersion of a d-dimensional distribution which are based on the volumes of simplices of dimension k≤d formed by k+1 independent copies and raised to some power δ. We study properties of extremal measures that maximize these functionals. In particular, for positive δ we characterize their support and for negative δ we establish connection with potential theory and motivate the application to space-filling design for computer experiments. Several illustrative examples are presented.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer Verlag
ISSN: 0932-5026
Date of Acceptance: 13 March 2016
Last Modified: 01 Nov 2022 10:00

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