3 papers
math.PR2021
On Negative Dependence Properties of Latin Hypercube Samples and Scrambled Nets
Benjamin Doerr, Michael Gnewuch
We study the notion of -negative dependence of random variables. This notion is a relaxation of the notion of negative orthant dependence (which corresponds to -negative depe…
math.ST2021
Discrepancy Bounds for a Class of Negatively Dependent Random Points Including Latin Hypercube Samples
Michael Gnewuch, Nils Hebbinghaus
We introduce a class of -negatively dependent random samples. We prove that this class includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin…
math.NA2019
On Negatively Dependent Sampling Schemes, Variance Reduction, and Probabilistic Upper Discrepancy Bounds
Michael Gnewuch, Marcin Wnuk, Nils Hebbinghaus
We study some notions of negative dependence of a sampling scheme that can be used to derive variance bounds for the corresponding estimator or discrepancy bounds for the underlyin…