Probabilistic Lower Bounds for the Discrepancy of Latin Hypercube Samples

Benjamin Doerr (), Carola Doerr () and Michael Gnewuch ()
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Benjamin Doerr: LIX - UMR 7161, École Polytechnique
Carola Doerr: UPMC Univ Paris 06, CNRS, LIP6 UMR 7606, Sorbonne Universités
Michael Gnewuch: Mathematisches Seminar, Christian-Albrechts-Universität Kiel

A chapter in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, pp 339-350 from Springer

Abstract: Abstract We provide probabilistic lower bounds for the star discrepancy of Latin hypercube samples. These bounds are sharp in the sense that they match the recent probabilistic upper bounds for the star discrepancy of Latin hypercube samples proved in Gnewuch and Hebbinghaus (Discrepancy bounds for a class of negatively dependent random points including Latin hypercube samples. Preprint 2016). Together, this result and our work implies that the discrepancy of Latin hypercube samples differs at most by constant factors from the discrepancy of uniformly sampled point sets.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-72456-0_16

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DOI: 10.1007/978-3-319-72456-0_16

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