最小低阶Lee矩混杂准则及其应用  

Minimum Lee-moment aberration and its applications

作　　者：邹娜[1] 覃红[2] 

机构地区：[1]中南财经政法大学统计与数学学院,武汉430073 [2]华中师范大学数学与统计学学院,武汉430079

出　　处：《中国科学：数学》2016年第1期97-110,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11301546;11271147和11471136);中南财经政法大学创新团队(批准号:31541511201)资助项目

摘　　要：众所周知,有多种准则可以用于比较和评价部分因析设计的优劣,在这些准则中,最小低阶矩混杂准则既简单明了,又计算量较小.但是,该准则中的各阶矩是基于任意两次试验之间的Hamming距离来定义的,由此导致了该准则具有一定的局限性.本文用Lee距离代替Hamming距离来定义新的矩,在此基础上提出了最小低阶Lee矩混杂准则,并用它来比较高水平部分因析设计的优劣.同时,本文通过建立最小低阶Lee矩混杂准则与其他设计筛选准则之间的解析关系,来验证这一新准则的统计合理性.Various criteria have been proposed to compare and assess fractional factorial designs. Among them the minimum moment aberration criterion is conceptually simple and computationally cheap. However, the power moments in the minimum moment aberration criterion depend on the Hamming distances between two runs, which leads to minimum moment aberration criterion having a few defects. In this paper, we use Lee distance instead of Hamming distance to define power moments, and propose the minimum Lee-moment aberration criterion to compare and assess multi-level fractional factorial designs. Some relationships between minimum Lee-moment aberration criterion and other criteria are also studied, which provides a significant statistical justification of minimum Lee-moment aberration criterion.

关 键 词：Lee距离 Lee矩 最小低阶矩混杂 均匀性 

分 类 号：O212[理学—概率论与数理统计]