线性模型下二水平正规设计效应混杂的度量  

The Confounding Measure of Effects in Two-Level Regular Designs under Linear Model

作　　者：李奥 李智 李智明[1] LI Ao;LI Zhi;LI Zhiming(College of Mathematics and System Science,Xinjiang University,Urumqi,830046,China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《应用概率统计》2024年第5期757-771,共15页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金(批准号:12061070);新疆维吾尔自治区自然科学基金(批准号:2021D01E13)资助。

摘　　要：在线性模型中,试验设计效应之间的混杂会导致参数估计存在某种偏差.针对二水平正规设计,本文引入混杂指标集来度量这类偏差,并提出一种新方法来研究其性质,揭示它与别名效应数型、别名关系数及字长型之间的关系,得到了低阶效应混杂指标的计算公式以及最优设计存在的一些必要条件,并通过例子展示了所得到的理论结果.In the design of experiments,the confounding of effects can cause the bias of parameter estimator in a linear model.This paper mainly proposes a confounding index for two-level regular designs to measure such bias.We introduce a new method to study the properties of the index and reveal the relationship between the confounding index,alias relation number,aliased component-number pattern,and word-length pattern.The confounding formula among lower-order effects is obtained to provide some conditions for optimal designs.Some examples are provided to illustrate the theoretical results.

关 键 词：二水平正规设计 线性回归模型 别名矩阵 混杂指标数 别名效应数型 

分 类 号：O212.6[理学—概率论与数理统计]