Enhancing the sample average approximation method with U designs

• 成果类型: Article
• 署名作者: Tang, Qi; Qian, Peter Z. G.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asq046
• 发表日期: 2010
• 页码: 947960
• 关键词: CENTRAL-LIMIT-THEOREM

摘要

Many computational problems in statistics can be cast as stochastic programs that are optimization problems whose objective functions are multi-dimensional integrals. The sample average approximation method is widely used for solving such a problem, which first constructs a sampling-based approximation to the objective function and then finds the solution to the approximated problem. Independent and identically distributed sampling is a prevailing choice for constructing such approximations. Recently it was found that the use of Latin hypercube designs can improve sample average approximations. In computer experiments, U designs are known to possess better space-filling properties than Latin hypercube designs. Inspired by this fact, we propose to use U designs to further enhance the accuracy of the sample average approximation method. Theoretical results are derived to show that sample average approximations with U designs can significantly outperform those with Latin hypercube designs. Numerical examples are provided to corroborate the developed theoretical results.