ASYMPTOTIC NORMALITY OF SCRAMBLED GEOMETRIC NET QUADRATURE

• 成果类型: Article
• 署名作者: Basu, Kinjal; Mukherjee, Rajarshi
• 署名单位: Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1508
• 发表日期: 2017
• 页码: 1759-1788
• 关键词: sequences; variance

摘要

In a very recent work, Basu and Owen [Found. Comput. Math. 17 (2017) 467-496] propose the use of scrambled geometric nets in numerical integration when the domain is a product of s arbitrary spaces of dimension d having a certain partitioning constraint. It was shown that for a class of smooth functions, the integral estimate has variance O(n(-1-2/d) (log n)(s-1)) for scrambled geometric nets compared to O(n(-1)) for ordinaryMonte Carlo. The main idea of this paper is to expand on the work by Loh [Ann. Statist. 31 (2003) 1282-1324] to show that the scrambled geometric net estimate has an asymptotic normal distribution for certain smooth functions defined on products of suitable subsets of R-d.