Probabilistic Lower Bounds for the Discrepancy of Latin Hypercube Samples
Numerical Analysis
2021-09-21 v1
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 [M.~Gnewuch, N.~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.
Keywords
Cite
@article{arxiv.1707.08481,
title = {Probabilistic Lower Bounds for the Discrepancy of Latin Hypercube Samples},
author = {Benjamin Doerr and Carola Doerr and Michael Gnewuch},
journal= {arXiv preprint arXiv:1707.08481},
year = {2021}
}