Probabilistic Lower Bounds for the Discrepancy of Latin Hypercube Samples

TL;DR

This paper establishes probabilistic lower bounds for the star discrepancy of Latin hypercube samples, showing they are close to the discrepancy of uniform samples, thus providing a comprehensive understanding of their discrepancy behavior.

Contribution

It introduces sharp probabilistic lower bounds for Latin hypercube discrepancy, matching recent upper bounds and demonstrating their discrepancy is comparable to uniform sampling.

Findings

Lower bounds match recent upper bounds

Discrepancy of Latin hypercube samples is close to uniform samples

Results imply constant-factor equivalence in discrepancy

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.