拓展设计及部分因析设计的空间填充性质

发布时间：2018-06-06 01:41

本文选题：拓展设计 + 均匀性　；参考：《华中师范大学》2015年硕士论文

【摘要】：随着科学技术的进步,亟待解决的复杂问题层出不穷,这给试验设计带来了新的机遇和挑战,可参见Bates et al. (1996).如何从众多的备选设计中选出合适的设计,并使它在某种意义下具有优良性质备受理论研究和实践应用的关注.因此,研究者们提出了许多设计筛选准则.在这众多的设计筛选准则中,均匀性准则和最小矩混杂准则具有优良的性质,被广泛采用,参见]Eang, Li and Sudjianto (2006)和Xu (2003).面对复杂的研究对象,一种很自然的试验策略就是采取序贯实验.实验者按照最初选定的设计进行实验,而在实验进行的过程中或在实验完成时又按照另一个设计进行了一部分补充实验,故整个实验阶段采用的设计由这前后两个设计共同构成,我们称其为拓展设计.这类设计即符合人类认识自然的规律,同时又时常应用于农业实验、工业实验以及计算机实验等众多领域.因此,研究拓展设计的性质具有重要意义.本文研究了拓展设计的空间填充性质,旨在为这类设计的应用提供必要的理论基础.本文的研究表明当初始设计选为均匀设计,附加设计尽可能均匀时,不但附加设计对初始设计均匀性的破坏最小,而且保证了拓展设计尽可能的均匀.在可卷型L2偏差和Lee偏差下,我们给出了拓展设计偏差的一个下界,这不仅可以为比较不同设计的均匀性提供一个公平的基准,同时可以大幅度提高计算机收索均匀拓展设计的效率.受均匀拓展设计的启发,我们证明了设计的Lee偏差可以表述为其频率向量的二次型,并建立了在Lee偏差下一般混水平设计与其补设计的关系.Cheng and Wu (2001)指出当因子的水平数超过2时,一个或者多个因子的水平置换将改变设计的几何结构,从而改变设计的统计性质.因此,高水平部分因析设计的空间填充性质近几年来越来越受到重视,参见Tang, Xu and Lin (2012), Zhou and Xu(2014).本文研究了最小矩混杂设计的空间填充性质.我们的结论表明在保持设计最小矩混杂性的基础上,水平置换改善了设计的空间填充性质.我们还建立了基于核函数定义的平均偏差与正交性准则之间的关系,这进一步丰富了平均偏差的统计评价.
[Abstract]:With the progress of science and technology, there are many complicated problems that need to be solved urgently. This brings new opportunities and challenges to experimental design. See Bates et al. In 1996. How to select a suitable design from many alternative designs and make it have good properties in a certain sense has attracted much attention from theoretical research and practical application. Therefore, many design screening criteria have been proposed. Among these design screening criteria, the uniformity criterion and the minimum moment hybrid criterion have excellent properties and are widely used. See] Eang, Li and Sudjianto / 2006) and Xu / 2003. In the face of complex research objects, a very natural test strategy is to adopt sequential experiments. The experimenter carried out the experiment according to the original design, and in the course of the experiment or at the time of the completion of the experiment, a part of the supplementary experiment was carried out according to another design. Therefore, the design used in the whole experiment stage is composed of the two designs before and after, which we call the extended design. This kind of design not only accords with the laws of human understanding of nature, but also is often used in many fields, such as agricultural experiments, industrial experiments and computer experiments. Therefore, it is of great significance to study the properties of extended design. In this paper, the space filling properties of extended design are studied in order to provide the necessary theoretical basis for the application of this kind of design. The research in this paper shows that when the initial design is chosen as uniform design and the additional design is as uniform as possible, not only the damage to the uniformity of the initial design is minimized by the additional design, but also the extended design is guaranteed to be as uniform as possible. In this paper, we give a lower bound of extended design deviation under the conditions of volume L2 deviation and Lee deviation, which can not only provide a fair benchmark for comparing the uniformity of different designs. At the same time, it can greatly improve the efficiency of the computer cable-receiving uniform expansion design. Inspired by the uniform extended design, we prove that the Lee deviation of the design can be expressed as the quadratic form of its frequency vector. The relation between the general mixing level design and its complementary design under Lee deviation is established. Cheng and Wu (2001) points out that the horizontal substitution of one or more factors will change the geometric structure of the design when the horizontal number of factors exceeds 2. In order to change the statistical nature of the design. Therefore, in recent years, more and more attention has been paid to the space filling properties of the high level design. See Tang, Xu and Lin / 2012, Zhou and / 2014. In this paper, the space filling property of minimum moment hybrid design is studied. Our conclusion shows that the horizontal displacement improves the space filling property of the design based on the minimum moment hybrid property of the design. We also establish the relationship between the average deviation and the orthogonality criterion based on the kernel function definition, which further enriches the statistical evaluation of the average deviation.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.6

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