The distribution of the discrepancy of scrambled digital (\(t\),\(m\),\(s\))-nets
type: Item
instance of: scholarly article
title: The distribution of the discrepancy of scrambled digital (\(t\),\(m\),\(s\))-nets
zbMATH Open document ID: 1020.65009
DOI: 10.1016/S0378-4754(02)00238-0
author: Hee Sun Hong
author: Fred J. Hickernell
author: Gang Wei
published in: Mathematics and Computers in Simulation
publication date: 2003-05-19T00:00:00Z
review text: The authors compare the empirical distribution of the squared discrepancy of scrambled digital \((t,m,s)\)-nets with the theoretical asymptotic normal distribution. More precisely, in Section 2 they provide a general description of the discrepancy and derive the theoretical asymptotic distribution of the square discrepancy of scrambled nets. Section~3 explains the procedure for fitting the empirical distribution of the square discrepancy of scrambled nets to the theoretical asymptotic distribution. Section~4 discusses the experimental results. Finally, Section~5 contains some concluding results. Furthermore, the authors discuss the variance and the empirical distribution of the square discrepancy of Owen's scrambling and a variant, linear scrambling.
Mathematics Subject Classification ID: 65C60
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 1912339
zbMATH Keywords: chi-square tests
zbMATH Keywords: empirical distribution
zbMATH Keywords: squared discrepancy of scrambled digital \((t,m,s)\)-nets
zbMATH Keywords: asymptotic distribution
zbMATH Keywords: fitting
zbMATH Keywords: quasi Monte Carlo method
zbMATH Keywords: experimental results
reviewed by: Jaromír Antoch
describes a project that uses: TOMS659
MaRDI profile type: Publication
cites work: Algorithm 659
cites work: The asymptotic efficiency of randomized nets for quadrature
cites work: Extensible Lattice Sequences for Quasi-Monte Carlo Quadrature
cites work: A generalized discrepancy and quadrature error bound
cites work: Q4934363
cites work: The price of pessimism for multidimensional quadrature
cites work: The Mean Square Discrepancy of Scrambled (t,s)-Sequences
cites work: On the asymptotic distribution of scrambled net quadrature.
cites work: On the \(L_2\)-discrepancy for anchored boxes
cites work: Q4718172
cites work: Q4226446
cites work: Q4856469
cites work: Q3996207
cites work: The discrepancy and gain coefficients of scrambled digital nets.
description: scientific article; zbMATH DE number 1912339