优先估计三阶交互效应的最优二水平正规设计

发布时间：2018-04-21 08:48

本文选题：混杂效应个数型 + 纯净效应　；参考：《东北师范大学》2016年硕士论文

【摘要】：试验设计是研究如何对观测对象进行观察以最有效地获得数据和进行数据分析的统计学分支,在统计学的发展中起着重要作用。在各类研究中,大多数响应变量往往受到多个因子的影响,因此涉及多因素的试验和观测问题是试验设计的主要研究课题。随着因子个数的增加,试验单元的个数指数地增长。当因子个数较多时完全因析试验往往超出物力、财力和时间的承受能力而不能实现,因而部分因析试验才常常是实际可行的。正因为这样,如何选择最优的部分因析设计及其数据分析方法成为统计学家重点关心的课题。Zhang et al.(2008)对正规设计分类提出一个新的模型,叫做混杂效应个数型(AENP),然后基于混杂效应个数型和效应排序原则(EHP)提出了一般最小低阶混杂(GMC)准则,用于选择最优设计。该准则得到的最优设计叫GMC设计。然而在实际试验中并不是所有情况都是主效应最重要的,有的时候试验者最关注的可能是因子的二阶或三阶交互效应。例如在很多化学实验中,试验者想特别知道三种及三种以上因素的化学效应。而不是首要知道一,二阶效应。在本文中,我们将对优先估计三阶交互效应的部分因析设计进行研究。我主要完成以下方面的一些工作：(1)针对优先估计三阶交互效应的要求,提出了一种新的效应混杂个数测度的排序准则,称为优先估计三阶交互因子的别名效应个数模型,记为U_3-AENP,并建立相应的最优性准则。把得到的最优设计称之为U_3-GMC设计。(2)给出在优先估计三阶交互效应原则下选最优设计的计算方法及例子。(3)进而提出在分区组2~(n-m)：2~r设计情形下优先估计三阶交互效应的准则并计算了当试验次数为16时的全部设计。(4)给出有关该最新准则和最优设计的一些基本理论结果和例子,并与GMC设计进行比较。最后,通过定义中的算法得出当试验次数为16,32时的这种全部最优设计,以及当试验次数为64时部分最优设计表,包括与GMC设计的比较。
[Abstract]:Experimental design is a branch of statistics that studies how to observe the observed objects in order to obtain and analyze the data effectively. It plays an important role in the development of statistics. In all kinds of research, most of the response variables are often affected by multiple factors, so the experimental and observation problems involving multiple factors are the main research topics of experimental design. As the number of factors increases, the number of experimental units increases exponentially. When the number of factors is more than that of material resources, financial resources and time, it can not be realized, so the partial factor analysis test is often practical and feasible. Because of this, how to select the optimal partial factorial design and its data analysis method has become the key topic of statisticians' concern. Zhang et al.2008) proposes a new model for the classification of regular design. The general minimum low order hybrid GMC (GMC) criterion is proposed for the selection of optimal design based on the number of hybrid effects and the EHPs. The optimal design obtained by this criterion is called GMC design. However, not all cases are the most important in practical experiments, sometimes the most important factor is the second-order or third-order interaction effect. In many chemical experiments, for example, the experimenters want to know the chemical effects of three or more factors. Rather than knowing first one, two-order effects. In this paper, we will study the partial factorial design for preferential estimation of third order interaction effects. I have mainly done some work in the following aspects: 1) in response to the requirement of priority estimation of third-order interaction effect, I propose a new ranking criterion for estimating the number of third order interaction factors, which is called the aliasing effect number model of first-order interaction factor estimation. It is described as USP-AENPs and the corresponding optimality criterion is established. The optimal design is called U_3-GMC design. 2) the calculation method and example of optimal design under the principle of priority estimation of third order interaction effect are given. Furthermore, in the case of partition group 2~(n-m):2~r design, priority estimation of third order interaction effect is proposed. The basic theoretical results and examples of the new criterion and optimal design are given when the number of tests is 16:00. And compared with GMC design. Finally, through the algorithm in the definition, all the optimal designs are obtained when the number of experiments is 16 ~ 32, and the partial optimal design table is obtained when the number of experiments is 64, including the comparison with the GMC design.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：C81

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