多水平试验设计中的广义Double方法  

Generalized Double Method for Designs with Multi-level

作　　者：邹娜[1] 勾廷勋 覃红 ZOU Na;GOU Tingxun;QIN Hong(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430074,China;School of Mathematics,Northwest University,Xi'an 710127,China;Faculty of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China)

机构地区：[1]中南财经政法大学统计与数学学院,武汉430074 [2]西北大学数学学院,西安710127 [3]华中师范大学数学与统计学学院,武汉430079

出　　处：《应用数学学报》2021年第6期856-868,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金面上基金(No.11871237);国家自然科学基金青年基金(No.11901455)资助项目;中南财经政法大学学科统筹建设项目(No.XKHJ202125).

摘　　要：Double方法主要用于构造具有较高分辨度的两水平设计,这一方法利用了传统的正负水平置换,简单且有效.对于多水平设计,由于水平置换不是唯一的,传统的Double方法不再适用.本文基于镜像映射提出了一种广义Double方法,在由Lee偏差度量的均匀性准则下讨论广义Double方法的合理性,并给出了广义Double设计Lee偏差的下界.数值计算结果显示这些下界是可以达到的,可作为构造和搜索最优Double设计的基准.Double method,which revers signs for some factors,is a simple but very powerful technique for constructing two-level fractional factorial designs with high resolution.However,this method is not suitable for studying on similar issues of design with multi-level due to level permutations being not only one.Based on mirror mapping,this paper proposes a generalized Double method to construct optimal generalized Double designs with multi-level,and discusses the rationality of this method under the uniformity criterion of Lee discrepancy.The lower bounds of the generalized Double design are provided.Numerical results sliow that these lower bounds are achievable,and can be used as a benchmark for constructing and searching for optimal Double designs.

关 键 词：镜像映射 广义Double Lee偏差 均匀性 下界 

分 类 号：O212.6[理学—概率论与数理统计]