Article Dans Une Revue Statistical Papers Année : 2016

Extremal measures maximizing functionals based on simplicial volumes

Résumé

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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A comme partie hal-01308316 Objet présenté à une conférence Luc Pronzato. A measure of dispersion based on average exponentiated volumes, with application in experimental design. ProbaStat'2015, Slovak Academy of Sciences/Comenius University, Bratislava, Jun 2015, Smolenice, Slovakia. ⟨hal-01308316⟩

Dates et 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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