On the asymptotic distribution of scrambled net quadrature

• 成果类型: Article
• 署名作者: Loh, WL
• 署名单位: National University of Singapore
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1059655914
• 发表日期: 2003
• 页码: 1282-1324
• 关键词: CENTRAL-LIMIT-THEOREM; variance; remainder

摘要

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.