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Probabilistic Lower Bounds for the Discrepancy of Latin Hypercube Samples

  • Benjamin Doerr
  • Carola Doerr
  • Michael GnewuchEmail author
Chapter

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.

Notes

Acknowledgements

The authors thank two anonymous referees for their comments which helped to improve the presentation of the paper.

Part of this work was done while Michael Gnewuch was visiting the Laboratoire d’Informatique (LIX) as Chercheur Invité of École Polytechnique. He likes to thank the colleagues from LIX for their hospitality.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.École PolytechniqueLIX - UMR 7161PalaiseauFrance
  2. 2.Sorbonne UniversitésUPMC Univ Paris 06, CNRS, LIP6 UMR 7606ParisFrance
  3. 3.Christian-Albrechts-Universität KielMathematisches SeminarKielGermany

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