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Extremal measures maximizing functionals based on simplicial volumes

Author

Listed:
  • Luc Pronzato

    (route des Lucioles, Les Algorithmes, bât. Euclide B)

  • Henry P. Wynn

    (London School of Economics)

  • Anatoly Zhigljavsky

    (Cardiff University
    Lobachevsky Nizhny Novgorod State University)

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.

Suggested Citation

  • Luc Pronzato & Henry P. Wynn & Anatoly Zhigljavsky, 2016. "Extremal measures maximizing functionals based on simplicial volumes," Statistical Papers, Springer, vol. 57(4), pages 1059-1075, December.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:4:d:10.1007_s00362-016-0767-6
    DOI: 10.1007/s00362-016-0767-6
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    References listed on IDEAS

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    1. Zhigljavsky, Anatoly & Dette, Holger & Pepelyshev, Andrey, 2010. "A New Approach to Optimal Design for Linear Models With Correlated Observations," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1093-1103.
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    Cited by:

    1. Luc Pronzato & Henry P. Wynn & Anatoly Zhigljavsky, 2019. "Bregman divergences based on optimal design criteria and simplicial measures of dispersion," Statistical Papers, Springer, vol. 60(2), pages 545-564, April.

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