一般最小低阶混杂设计的统计性质  

The Statistical Properties of General Minimum Lower-order Confounding Designs

作　　者：周琦 刘盼盼 ZHOU QI;LIU PANPAN(School of Statistics,Tianjin University of Finance and Economics,Tianjin 300222,China)

机构地区：[1]天津财经大学统计学院,天津300222

出　　处：《应用数学学报》2022年第1期19-30,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11971345,11501405,11601366,11701088);天津市“131”人才工程;天津市中青年骨干创新人才培养计划资助项目。

摘　　要：本文旨在研究满足N/4+2≤n≤5N/16的GMC 2^(n-m)设计的统计性质(N=2^(n-m)),首先通过研究这些设计别名关系来讨论其估计能力,然后提出了一种新的理论方法用以得到这些设计的混杂信息,最后给出了可供实际使用的试验表格.Two-level factorial designs are widely used in various scientific experiments.To satisfy the requirement of these designs for practical applications,the general minimum lower order confounding(GMC)criterion was proposed to select factorial designs,called GMC designs.The theoretical construction results of GMC 2^(n-m) designs with N/4+2≤n≤5 N/16 are proposed,where 2^(n-m) is used to denote the two-level fractional factorial designs with n factors and N(=2^(n-m))runs.This paper aims at studying the statistical properties of GMC 2^(n-m) designs with N/4+2≤n≤5 N/16.At first,we study the properties of the aliasing relations of these GMC designs.Then,we provide some results to illustrate the estimability of them,propose a new theoretical method to obtain their aliasing information and list the table containing the considered designs with the information of their statistical properties.Finally,we make the conclusion of this paper and discuss some future work.

关 键 词：因子设计 别名效应数模型 一般最小低阶混杂 

分 类 号：O212.6[理学—概率论与数理统计]