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Loh, Wei-Liem

On the asymptotic distribution of scrambled net quadrature. (English) Zbl 1105.62304

Ann. Stat. 31, No. 4, 1282-1324 (2003).
Summary: 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.

Cited in 1 Review
Cited in 18 Documents

MSC:

62E20 Asymptotic distribution theory in statistics
65C05 Monte Carlo methods
65C60 Computational problems in statistics (MSC2010)
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Full Text: DOI Euclid

References:

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