The Annals of Statistics

On the asymptotic distribution of scrambled net quadrature

Wei-Liem Loh

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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.

Article information

Ann. Statist., Volume 31, Number 4 (2003), 1282-1324.

First available in Project Euclid: 31 July 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62E05
Secondary: 62D05: Sampling theory, sample surveys 65C05: Monte Carlo methods

Asymptotic normality computer experiment numerical integration quasi-Monte Carlo scrambled net Stein's method


Loh, Wei-Liem. On the asymptotic distribution of scrambled net quadrature. Ann. Statist. 31 (2003), no. 4, 1282--1324. doi:10.1214/aos/1059655914.

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