Please use this identifier to cite or link to this item: https://doi.org/10.1214/aos/1059655914
Title: On the asymptotic distribution of scrambled net quadrature
Authors: Loh, W.-L. 
Keywords: Asymptotic normality
Computer experiment
Numerical integration
Quasi-Monte Carlo
Scrambled net
Stein's method
Issue Date: Aug-2003
Citation: Loh, W.-L. (2003-08). On the asymptotic distribution of scrambled net quadrature. Annals of Statistics 31 (4) : 1282-1324. ScholarBank@NUS Repository. https://doi.org/10.1214/aos/1059655914
Abstract: 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.
Source Title: Annals of Statistics
URI: http://scholarbank.nus.edu.sg/handle/10635/105267
ISSN: 00905364
DOI: 10.1214/aos/1059655914
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