Designs for crossvalidating approximation models

• 成果类型: Article
• 署名作者: Zhang, Qiong; 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/ast034
• 发表日期: 2013
• 页码: 9971004
• 关键词: latin hypercube designs; computer experiments; quantitative factors; Input variables; CONSTRUCTION; prediction

摘要

Multifold crossvalidation is routinely used for assessing the prediction error of an approximation model for a black-box function. Despite its popularity, this method is known to have high variability. To mitigate this drawback, we propose an experimental design approach that borrows Latin hypercube designs to construct a structured crossvalidation sample such that the input values in each fold achieve uniformity. Theoretical results show that the estimate of the prediction error of the proposed method has significantly smaller variability than its counterpart under independent and identically distributed sampling. Numerical examples corroborate the theoretical results.