具有特定纯净效应折中设计的若干理论及构造  

Some theoretical results and constructions of compromise designs with specified sets of clear effects

作　　者：王东莹 张润楚[2,3] Dongying Wang;Runchu Zhang

机构地区：[1]吉林财经大学统计学院,长春130117 [2]南开大学数学科学学院,天津100002 [3]东北师范大学数学与统计学院,长春130024

出　　处：《中国科学：数学》2021年第5期763-772,共10页Scientia Sinica：Mathematica

摘　　要：许多因析试验中,试验者只关心指定的一部分因子效应的估计效果.针对此类问题,Addelman(1962)首次提出了折中设计的方法,并定义纯净折中设计以保证指定的因子效应被有效地估计出来,但此类纯净折中设计的分辨度限定Ⅲ为Ⅳ.本文研究了四类全新的折中设计,指定因子效应的集合分别记为{G_(1);G_(1)×G_(1)}、{G_(1);G_(1)×G_(1);G_(2)×G_(2)}、{G_(1);G_(1)×G_(1);G_(1)×G_(2)}和{G_(1);G_(1)×G_(2)}.相应地,可以定义四种类型的纯净折中设计,即指定因子效应全部纯净的设计.本文研究四类纯净折中设计的存在性和结构特性,给出一些理论结果和具体的构造方法.构造结果表明新型的纯净折中设计的分辨度为Ⅲ或Ⅳ,并且与Addelman(1962)提出的纯净折中设计相比具有更多的纯净两阶交互效应.In many practical experiments,the experimenter is only interested in the estimation of a few of specified factor effects.The designs that are suitable to achieve such purposes are called compromise plans,which were first studied by Addelman(1962).Clear compromise plans allow the estimation of specified factor effects,but the resolution is limited to IV.In this paper,we study four classes of compromise designs,with specified effects denoting as {G_(1);G_(1)×G_(1)}、{G_(1);G_(1)×G_(1);G_(2)×G_(2)}、{G_(1);G_(1)×G_(1);G_(1)×G_(2)}and {G_(1);G_(1)×G_(2)},respectively.Clear compromise design,that is compromise design with these specified effects being clear,can be of resolution Ⅲ or Ⅳ.We give the existence and characteristics of clear compromise designs of classes one to four,and provide some theoretic results and constructions of clear compromise designs.Compared with the clear compromise plan,the proposed clear compromise design has more clear two factor interactions.

关 键 词：折中设计 纯净效应 部分因析设计 

分 类 号：O212.6[理学—概率论与数理统计]