最优折衷设计及其构造

发布时间：2018-03-03 17:54

  本文选题：折衷设计　切入点：别名效应个数型　出处：《东北师范大学》2017年博士论文　论文类型：学位论文

【摘要】：因析设计如今已经广泛应用到很多领域,如工业、农业、临床试验、社会经济以及相当多的其他领域。对于不同的试验而言,试验者会有着不同的目的,因此也就需要不同类型的最优设计来安排试验。特别地,在很多时候,试验者的目的是想要估计一部分特定因子效应,那么此时他们就需要为试验选择一种特别的最优设计。Addelman(2012)[1]首次提出折衷设计的概念,折衷设计是介于正交主效应设计和可以非相关估计主效应和所有两因子交互效应设计之间的一种设计,并在其文章中提出了三种类型的两水平折衷设计,Sun(1994)[45]又提出了第四种类型的折衷设计。这四种类型的折衷设计所估计的特定两因子交互效应具有以下的形式:1.{G_1 ×G_1}, 2.{G_1 ×G_1, G_2×G_2}, 3.{G_1×G_1, G_1 ×G_2}, 4.{G_1 ×G_2},其中,{G_1 : G_2}是试验中n个因子的某一种划分,Gi×Gj表示Gi中的因子和Gj(i,j = 1,2)中的因子之间两因子交互效应的集合。本篇论文在以上背景的基础上,对最优折衷设计及其构造进行了研究,主要做了以下工作:·首先将折衷设计的概念进行扩展。一个设计叫做折衷设计,如果它可以估计任意一个特定效应的集合。特别地,我们提出了新的折衷设计分类:1. {G_1, G_1×G_1}, 2.{G_1, G_1 ×G_1, G_2×G_2}, 3. {G_1,G_1 ×G_1,G_1×G_2},4.{G_1, G_1 ×G_2}.·在四阶及以上效应都可以忽略的弱假设下来寻找最优设计,并针对分辨度Ⅲ及以上的设计提出一个新的分类工具部分别名效应个数型(Partial Aliased Effect Number Pattern,简称P-AENP)用来研究最优折衷设计的选择和构造。利用P-AENP选出了第一类和第四类纯净折衷设计、强纯净折中设计以及一般最优折衷设计并得到了一些理论结果。·利用变量分辨度设计以及广义变量分辨度设计,给出强纯净折衷设计存在的必要条件以及构造方法。
[Abstract]:Because design is now widely used in many fields, such as industry, agriculture, clinical trials, socio-economic, and quite a few other fields. For different trials, the experimenters have different purposes. So different types of optimal designs are needed to arrange the trials. In particular, in many cases, the purpose of the experimenters is to estimate a certain part of the factor effect. At this point, they need to choose a particular optimal design for the experiment. Addelmant2012) [1] for the first time, they put forward the concept of compromise design. The tradeoff design is a design between the orthogonal principal effect design and the design with which the principal effect can be independently estimated and all the two factor interaction effects are designed. In his paper, three types of two-level compromise designs are proposed [45] and 4th types of compromise designs are proposed. The specific two-factor interaction effects estimated by these four types of compromise designs have the following form: 1. {G1 脳 G1}, 2. * G1, G2 脳 GSHANG2}, 3. {G _ S _ 1 脳 G _ 1, G _ 1 脳 G _ 2}, 4. {G _ 1 脳 G _ 2}, where, {G _ S _ 1: G _ 2} is one of the several factors in the experiment, which is a collection of two factors that divide the interaction effect between the factors in Gi and those in Gji _ j _ j = 1 ~ 2. This paper, on the basis of the above background, is a collection of the two factors of interaction between the factors in the Gi and the ones in the Gji _ j _ j _ _ _. In this paper, the optimal compromise design and its construction are studied. The main works are as follows: first, the concept of compromise design is extended. A design is called a compromise design, if it can estimate the set of any particular effect. We have proposed a new eclectic design classification: 1: 1.{ G _ 1s _ _ _. A new classification tool named partial Aliased Effect Number pattern (P-AENPN) is proposed for the design of resolution 鈪，

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