Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands

DOI10.1214/11-AOS880zbMath1298.65011arXiv1007.0842MaRDI QIDQ638795

Josef Dick

Publication date: 14 September 2011

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.0842

zbMATH Keywords

randomized quasi-Monte Carlo methodsexact convergence ratedigital \((t,m,s)\)-netsOwen's scrambling on order \(d\)root mean square worst-case error

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Numerical integration (65D30) Well-distributed sequences and other variations (11K36) Pseudo-random numbers; Monte Carlo methods (11K45)

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Cites Work

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• The mean square discrepancy of randomized nets
• Monte Carlo Variance of Scrambled Net Quadrature
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