The distribution of the discrepancy of scrambled digital (t, m, s)-nets

Hee Sun Hong; Fred J. Hickernell; Gang Wei

doi:10.1016/S0378-4754(02)00238-0

The distribution of the discrepancy of scrambled digital (t, m, s)-nets

Hee Sun Hong^*, Fred J. Hickernell, Gang Wei

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Conference article › peer-review

4 Citations (Scopus)

Abstract

Owen proposed a method of scrambling (t, m, s)-nets to eliminate statistical bias while retaining the low discrepancy property. Recently a central limit theorem has been proved for scrambled net quadrature. This article compares the empirical distribution of the square discrepancy of scrambled digital (t, m, s)-nets with the theoretical asymptotic distribution suggested by the central limit theorem. Furthermore this article discusses the variance and the empirical distribution of the square discrepancy of Owen's scrambling and a variant, linear scrambling.

Original language	English
Pages (from-to)	335-345
Number of pages	11
Journal	Mathematics and Computers in Simulation
Volume	62
Issue number	3-6
DOIs	https://doi.org/10.1016/S0378-4754(02)00238-0
Publication status	Published - 3 Mar 2003
Event	3rd IMACS Seminar on Monte Carlo Methods - Salzburg, Austria Duration: 10 Sept 2001 → 14 Sept 2001 http://mcm2001.sbg.ac.at/

Scopus Subject Areas

Theoretical Computer Science
Computer Science(all)
Numerical Analysis
Modelling and Simulation
Applied Mathematics

User-Defined Keywords

(t, s)-Sequences
Asymptotically normal
Chi-square
Empirical distribution

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10.1016/S0378-4754(02)00238-0

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abstract = "Owen proposed a method of scrambling (t, m, s)-nets to eliminate statistical bias while retaining the low discrepancy property. Recently a central limit theorem has been proved for scrambled net quadrature. This article compares the empirical distribution of the square discrepancy of scrambled digital (t, m, s)-nets with the theoretical asymptotic distribution suggested by the central limit theorem. Furthermore this article discusses the variance and the empirical distribution of the square discrepancy of Owen's scrambling and a variant, linear scrambling.",

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T1 - The distribution of the discrepancy of scrambled digital (t, m, s)-nets

AU - Hong, Hee Sun

AU - Hickernell, Fred J.

AU - Wei, Gang

PY - 2003/3/3

Y1 - 2003/3/3

N2 - Owen proposed a method of scrambling (t, m, s)-nets to eliminate statistical bias while retaining the low discrepancy property. Recently a central limit theorem has been proved for scrambled net quadrature. This article compares the empirical distribution of the square discrepancy of scrambled digital (t, m, s)-nets with the theoretical asymptotic distribution suggested by the central limit theorem. Furthermore this article discusses the variance and the empirical distribution of the square discrepancy of Owen's scrambling and a variant, linear scrambling.

AB - Owen proposed a method of scrambling (t, m, s)-nets to eliminate statistical bias while retaining the low discrepancy property. Recently a central limit theorem has been proved for scrambled net quadrature. This article compares the empirical distribution of the square discrepancy of scrambled digital (t, m, s)-nets with the theoretical asymptotic distribution suggested by the central limit theorem. Furthermore this article discusses the variance and the empirical distribution of the square discrepancy of Owen's scrambling and a variant, linear scrambling.

KW - (t, s)-Sequences

KW - Asymptotically normal

KW - Chi-square

KW - Empirical distribution

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U2 - 10.1016/S0378-4754(02)00238-0

DO - 10.1016/S0378-4754(02)00238-0

M3 - Conference article

AN - SCOPUS:0037417063

SN - 0378-4754

VL - 62

SP - 335

EP - 345

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

IS - 3-6

T2 - 3rd IMACS Seminar on Monte Carlo Methods

Y2 - 10 September 2001 through 14 September 2001

ER -

The distribution of the discrepancy of scrambled digital (t, m, s)-nets

Abstract

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