Extremal measures maximizing functionals based on simplicial volumes

Luc Pronzato (), Henry P. Wynn () and Anatoly Zhigljavsky ()
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Luc Pronzato: route des Lucioles, Les Algorithmes, bât. Euclide B
Henry P. Wynn: London School of Economics
Anatoly Zhigljavsky: Cardiff University

Statistical Papers, 2016, vol. 57, issue 4, No 12, 1059-1075

Abstract: Abstract We consider functionals measuring the dispersion of a d-dimensional distribution which are based on the volumes of simplices of dimension $$k\le d$$ k ≤ d formed by $$k+1$$ k + 1 independent copies and raised to some power $$\delta $$ δ . We study properties of extremal measures that maximize these functionals. In particular, for positive $$\delta $$ δ we characterize their support and for negative $$\delta $$ δ we establish connection with potential theory and motivate the application to space-filling design for computer experiments. Several illustrative examples are presented.

Keywords: Potential theory; Logarithmic potential; Computer experiments; Space-filling design; 62K05; 31C15 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00362-016-0767-6

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