A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments

• 成果类型: Article
• 署名作者: Loh, Wei-Liem
• 署名单位: National University of Singapore
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS530
• 发表日期: 2008
• 页码: 1983-2023
• 关键词: monte-carlo variance; CONVERGENCE

摘要

Let f : [0, 1)(d) -> R be an integrable function. An objective of many computer experiments is to estimate integral(d)([0, 1)) f (x) dx by evaluating f at a finite number of points in [0, 1)(d). There is a design issue in the choice of these points and a popular choice is via the use of randomized orthogonal arrays. This article proves a multivariate central limit theorem for a class of randomized orthogonal array sampling designs [Owen Statist. Sinica 2 (1992a) 439-452] as well as for a class of OA-based Latin hypercubes.