A CENTRAL LIMIT THEOREM FOR GENERAL ORTHOGONAL ARRAY BASED SPACE-FILLING DESIGNS

• 成果类型: Article
• 署名作者: He, Xu; Qian, Peter Z. G.
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1231
• 发表日期: 2014
• 页码: 1725-1750
• 关键词: variance

摘要

Orthogonal array based space-filling designs (Owen [Statist. Sinica 2(1992a) 439-452]; Tang [J. Amer. Statist. Assoc. 88 (1993) 1392-1397]) have become popular in computer experiments, numerical integration, stochastic optimization and uncertainty quantification. As improvements of ordinary Latin hypercube designs, these designs achieve stratification in multi-dimensions. If the underlying orthogonal array has strength t, such designs achieve uniformity up to t dimensions. Existing central limit theorems are limited to these designs with only two-dimensional stratification based on strength two orthogonal arrays. We develop a new central limit theorem for these designs that possess stratification in arbitrary multi-dimensions associated with orthogonal arrays of general strength. This result is useful for building confidence statements for such designs in various statistical applications.