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Extremal measures maximizing functionals based on simplicial volumes

Pronzato, Luc, Wynn, Henry P. ORCID: 0000-0002-6448-1080 and Zhigljavsky, Anatoly (2016) Extremal measures maximizing functionals based on simplicial volumes. Statistical Papers, 57 (4). pp. 1059-1075. ISSN 0932-5026

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Identification Number: 10.1007/s00362-016-0767-6


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
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Additional Information: © 2016 Springer International Publishing AG, Part of Springer Science and Business Media
Divisions: Centre for Analysis of Time Series
Subjects: Q Science > QA Mathematics
Date Deposited: 16 May 2016 11:59
Last Modified: 16 May 2024 02:17

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