Probabilistic Lower Bounds for the Discrepancy of Latin Hypercube Samples
For researchers in quasi-Monte Carlo methods, this work establishes tight theoretical bounds for Latin hypercube sampling, confirming its equivalence to uniform sampling in terms of discrepancy up to constant factors.
This paper proves probabilistic lower bounds for the star discrepancy of Latin hypercube samples that match existing upper bounds, showing that the discrepancy of Latin hypercube samples differs from that of uniformly random points by at most constant factors.
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.