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Extremal measures maximizing functionals based on simplicial volumes

Pronzato, Luc, Wynn, Henry P. 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: 20 Aug 2021 01:00

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