Measuring the quality of maximin space-filling designs
Résumé
We present here a new index for measuring the quality of maximin space-filling design for computer experiments. This index is based on a very accurate approximation of the distribution of the minimum distance for uniform designs. Expressions are explicitly given in terms of closed polynomial forms for any Lp distances, including L2, L1 and Chebyshev distances. When the size of the design or the dimension of the space is large, approximations through extreme value theory are exhibited. Some illustrations of our index are presented on simulated data and on a real problem.
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