Extremal measures maximizing functionals based on simplicial volumes
We consider functionals measuring the dispersion of a d-dimensional distribution which are based on the volumes of simplices of dimension \(k\le d\) formed by \(k+1\) independent copies and raised to some power \(\delta \). We study properties of extremal measures that maximize these functionals. In particular, for positive \(\delta \) we characterize their support and for negative \(\delta \) we establish connection with potential theory and motivate the application to space-filling design for computer experiments. Several illustrative examples are presented.
KeywordsPotential theory Logarithmic potential Computer experiments Space-filling design
Mathematics Subject Classification62K05 31C15
- Audze P, Eglais V (1977) New approach for planning out of experiments. Probl Dyn Strengths 35:104–107Google Scholar
- Fedorov VV (1972) Theory of optimal experiments. Academic Press, New YorkGoogle Scholar
- Pronzato L, Pázman A (2013) Design of experiments in nonlinear models. Asymptotic normality, optimality criteria and small-sample properties. LNS 212, Springer, New YorkGoogle Scholar
- Pronzato L, Wynn HP, Zhigljavsky A (2016) Extended generalised variances, with applications. Bernoulli (to appear). arXiv preprint arXiv:1411.6428