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

Hee Sun Hong, Fred J. Hickernell and Gang Wei

Mathematics and Computers in Simulation (MATCOM), 2003, vol. 62, issue 3, 335-345

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.

Keywords: Asymptotically normal; Chi-square; Empirical distribution; (t,s)-Sequences (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:62:y:2003:i:3:p:335-345

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

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