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August 2003 On the asymptotic distribution of scrambled net quadrature
Wei-Liem Loh
Ann. Statist. 31(4): 1282-1324 (August 2003). DOI: 10.1214/aos/1059655914


Recently, in a series of articles, Owen proposed the use of scrambled (t.m.s) nets and (t.s) sequences in high-dimensional numerical integration. These scrambled nets and sequences achieve the superior accuracy of equidistribution methods while allowing for the simpler error estimation techniques of Monte Carlo methods. The main aim of this article is to use Stein's method to study the asymptotic distribution of the scrambled (0.m.s) net integral estimate. In particular, it is shown that, for suitably smooth integrands on the s-dimensional unit hypercube, the estimate has an asymptotic normal distribution.


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Wei-Liem Loh. "On the asymptotic distribution of scrambled net quadrature." Ann. Statist. 31 (4) 1282 - 1324, August 2003.


Published: August 2003
First available in Project Euclid: 31 July 2003

zbMATH: 1105.62304
MathSciNet: MR2001651
Digital Object Identifier: 10.1214/aos/1059655914

Primary: 62E05
Secondary: 62D05 , 65C05

Keywords: asymptotic normality , computer experiment , numerical integration , quasi-Monte Carlo , scrambled net , Stein's method

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 4 • August 2003
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