本文選題：拓展設計 + 均勻性��； 參考：《華中師范大學》2015年碩士論文

【摘要】：隨著科學技術的進步,亟待解決的復雜問題層出不窮,這給試驗設計帶來了新的機遇和挑戰(zhàn),可參見Bates et al. (1996).如何從眾多的備選設計中選出合適的設計,并使它在某種意義下具有優(yōu)良性質(zhì)備受理論研究和實踐應用的關注.因此,研究者們提出了許多設計篩選準則.在這眾多的設計篩選準則中,均勻性準則和最小矩混雜準則具有優(yōu)良的性質(zhì),被廣泛采用,參見]Eang, Li and Sudjianto (2006)和Xu (2003).面對復雜的研究對象,一種很自然的試驗策略就是采取序貫實驗.實驗者按照最初選定的設計進行實驗,而在實驗進行的過程中或在實驗完成時又按照另一個設計進行了一部分補充實驗,故整個實驗階段采用的設計由這前后兩個設計共同構(gòu)成,我們稱其為拓展設計.這類設計即符合人類認識自然的規(guī)律,同時又時常應用于農(nóng)業(yè)實驗、工業(yè)實驗以及計算機實驗等眾多領域.因此,研究拓展設計的性質(zhì)具有重要意義.本文研究了拓展設計的空間填充性質(zhì),旨在為這類設計的應用提供必要的理論基礎.本文的研究表明當初始設計選為均勻設計,附加設計盡可能均勻時,不但附加設計對初始設計均勻性的破壞最小,而且保證了拓展設計盡可能的均勻.在可卷型L2偏差和Lee偏差下,我們給出了拓展設計偏差的一個下界,這不僅可以為比較不同設計的均勻性提供一個公平的基準,同時可以大幅度提高計算機收索均勻拓展設計的效率.受均勻拓展設計的啟發(fā),我們證明了設計的Lee偏差可以表述為其頻率向量的二次型,并建立了在Lee偏差下一般混水平設計與其補設計的關系.Cheng and Wu (2001)指出當因子的水平數(shù)超過2時,一個或者多個因子的水平置換將改變設計的幾何結(jié)構(gòu),從而改變設計的統(tǒng)計性質(zhì).因此,高水平部分因析設計的空間填充性質(zhì)近幾年來越來越受到重視,參見Tang, Xu and Lin (2012), Zhou and Xu(2014).本文研究了最小矩混雜設計的空間填充性質(zhì).我們的結(jié)論表明在保持設計最小矩混雜性的基礎上,水平置換改善了設計的空間填充性質(zhì).我們還建立了基于核函數(shù)定義的平均偏差與正交性準則之間的關系,這進一步豐富了平均偏差的統(tǒng)計評價.
[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.
【學位授予單位】：華中師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O212.6

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