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

Authors:
Hee Sun Hong;Fred J. Hickernell;Gang Wei
Affiliations:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China
Venue:
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Year:
2003

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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.