Probabilistic Lower Bounds for the Discrepancy of Latin Hypercube Samples

DOI10.1007/978-3-319-72456-0_16zbMath1405.65089arXiv1707.08481OpenAlexW2737288657MaRDI QIDQ4611807

Carola Doerr, Michael Gnewuch, Benjamin Doerr

Publication date: 22 January 2019

Published in: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.08481

Mathematics Subject Classification ID

Sampling theory, sample surveys (62D05) Orthogonal arrays, Latin squares, Room squares (05B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (7)

Star discrepancy subset selection: problem formulation and efficient approaches for low dimensions ⋮ A sharp discrepancy bound for jittered sampling ⋮ Note on pairwise negative dependence of randomly shifted and jittered rank-1 lattices ⋮ An elementary proof of a lower bound for the inverse of the star discrepancy ⋮ On negative dependence properties of Latin hypercube samples and scrambled nets ⋮ Discrepancy bounds for a class of negatively dependent random points including Latin hypercube samples ⋮ A generalized Faulhaber inequality, improved bracketing covers, and applications to discrepancy

Cites Work

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• A lower bound for the discrepancy of a random point set
• A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code
• The inverse of the star-discrepancy depends linearly on the dimension
• On tractability of weighted integration over bounded and unbounded regions in ℝ^{𝕤}
• Probability Inequalities for Sums of Bounded Random Variables
• High-dimensional integration: The quasi-Monte Carlo way

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