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Journal Articles Statistical Papers Year : 2016

Extremal measures maximizing functionals based on simplicial volumes

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.
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Dates and versions

hal-01308116 , version 1 (27-04-2016)

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Luc Pronzato, Henry P. Wynn, Anatoly A. Zhigljavsky. Extremal measures maximizing functionals based on simplicial volumes. Statistical Papers, 2016, 57 (4), pp.1059-1075. ⟨10.1007/s00362-016-0767-6⟩. ⟨hal-01308116⟩
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