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 . pp. 1-17. ISSN 0932-5026

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Abstract

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
Official URL:	http://link.springer.com/journal/362
Additional Information:	© 2016 Springer International Publishing AG, Part of Springer Science and Business Media
Library of Congress subject classification:	Q Science > QA Mathematics
Sets:	Research centres and groups > Centre for the Analysis of Time Series (CATS) Research centres and groups > Decision Support and Risk Group (DSRG)
Date Deposited:	16 May 2016 11:59
URL:	http://eprints.lse.ac.uk/66522/

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