Improved bounds for the bracketing number of orthants or revisiting an algorithm of Thiémard to compute bounds for the star discrepancy

DOI10.1016/j.jco.2024.101855MaRDI QIDQ6540045

Michael Gnewuch

Publication date: 15 May 2024

Published in: Journal of Complexity (Search for Journal in Brave)

zbMATH Keywords

discrepancypacking numbercovering numbertractabilityentropy numberdelta cover

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Irregularities of distribution, discrepancy (11K38) Pseudo-random numbers; Monte Carlo methods (11K45)

Cites Work

• Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo
• On the tractability of multivariate integration and approximation by neural networks
• Construction of minimal bracketing covers for rectangles
• Central limit theorems for empirical measures
• Sphere packing numbers for subsets of the Boolean \(n\)-cube with bounded Vapnik-Chervonenkis dimension
• An algorithm to compute bounds for the star discrepancy
• Weak convergence and empirical processes. With applications to statistics
• On the inverse of the discrepancy for infinite dimensional infinite sequences
• Expected dispersion of uniformly distributed points
• Discrepancy bounds for a class of negatively dependent random points including Latin hypercube samples
• Bracketing numbers for axis-parallel boxes and applications to geometric discrepancy
• Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo
• Probabilistic Star Discrepancy Bounds for Double Infinite Random Matrices
• A Remark on Stirling's Formula
• 3. On negatively dependent sampling schemes, variance reduction, and probabilistic upper discrepancy bounds
• An Upper Bound of the Minimal Dispersion via Delta Covers
• High-Dimensional Probability
• A generalized Faulhaber inequality, improved bracketing covers, and applications to discrepancy
• Calculation of Discrepancy Measures and Applications
• Entropy, Randomization, Derandomization, and Discrepancy
• Probabilistic discrepancy bound for Monte Carlo point sets
• Combinatorial methods in density estimation

Related Items (1)

Heuristic approaches to obtain low-discrepancy point sets via subset selection

This page was built for publication: Improved bounds for the bracketing number of orthants or revisiting an algorithm of Thiémard to compute bounds for the star discrepancy