LATTICE SAMPLING REVISITED - MONTE-CARLO VARIANCE OF MEANS OVER RANDOMIZED ORTHOGONAL ARRAYS

• 成果类型: Article
• 署名作者: OWEN, A
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325504
• 发表日期: 1994
• 页码: 930-945
• 关键词: computer

摘要

Randomized orthogonal arrays provide good sets of input points for exploration of computer programs and for Monte Carlo integration. In 1954, Patterson gave a formula for the randomization variance of the sample mean of a function evaluated at the points of an orthogonal array. That formula is incorrect for most of the arrays that are practical for computer experiments. In this paper we correct Patterson's formula. We also remark on a defect, related tb coincidences, in some orthogonal arrays. These are arrays of the farm OA(2q(2), 22 + 1, q, 2), where q is a prime power, obtained by constructions due to Bose and Bush and to Addelman and Kempthorne. we conjecture that subarrays of the form OA(2q(2), 2q, q, 2) may be constructed to avoid this defect.