【作者】 王丽丽；

【导师】 万建平；

【作者基本信息】 华中科技大学 ， 概率论与数理统计， 2005， 硕士

【摘要】 在数理统计学中,转变点问题是一门较新的课题。一般认为转变点问题的研究始于Page(1954)在Biometrika 上发表的一篇关于连续抽样检验的文章,早期的转变点问题主要研究工业自动控制中的一些问题。20 世纪60 年代后期,更多的统计学者,投入到这一研究领域,发表了一批有关转变点理论和应用的学术论文。特别是近二十年来,转变点的研究在理论和应用方面都有了快速的发展。在理论上,已有了一系列较记为成熟的结果,Csorgo and Horvath(1997)的专著“Limit theorems in change-points analysis”,就是对这一领域近二十年来理论的总结。转变点理论是统计推断的中心问题之一,由于转变点问题常常涉及到非独立随机变量分布的问题,这是非常难以处理的,所以这个问题的研究在理论上难度很大,更富有挑战性。一些处理转变点问题的方法也不断完善起来,如极大似然法,(加权)最小二乘法,非参数方法和Bayes 方法等等。在应用方面,现已发展到在经济、金融、医学和气象等诸方面都有大量的应用背景。本文主要讨论了几种模型的转变点问题及其应用。首先利用线性回归模型分析改革开放以来我国居民储蓄与收入的关系,并引入转变点理论研究二者关系发生结构性转变的问题; 接着将贝叶斯方法和信息准则方法相结合,检测了来自指数族分布的独立序列的转变点问题; 在分析中考虑到了指数族的共轭先验,得到了转变点的Schwarz 贝叶斯信息准则。因为共轭先验中包含超参数,在应用中将用ML—Ⅱ方法来估计它们; 随后,讨论了结构模型中参数只有一个转变点的检验和估计问题,基于最小信息准则原理,利用Schwarz 信息准则(SIC),在多余参数已知和未知的情况下分别给出了检验统计量; 最后利用Lajors Horvath 给出的方法,估计了日美汇率数据的均值转变点。更多还原

【Abstract】 In the mathematical statistics, the research of change points is a new problem comparatively. Commonly, it was thought that the research of change points started in 1954, when Page published a thesis about continuous sampling inspection in Biometrika. The change point problems appeared early in industry automation. Subsequently, many statisticians devoted into this research field, and some theoretic and applied papers about the change points were published. Now, a great deal mature results about the change point problems have been published, for example, Csorgo and Horváth “Limit theorem in change-points analysis ”in 1997,that is a theory research sum up recently. Some research methods of the change point problem are continually developed, for example, the maximum likelihood method, (weighted) least square method, the non-parametric method and Bayasian method etc. change point problems occur not only in industry automation early, but also in many natural and social fields such as economics, finance, medicine and meteorology etc. In this paper, we first use the linear regression model to analyze the relation of the residents’deposit and income, and introduce change point analysis to study the problem of the relation has structural change in an unknown time point.; then we use a Bayesian analysis and an information approach to detect a change-point in a sequence of independent random variables from exponential family distributions. The Bayesian Schwarz information criterion is derived. After that, we discuss the hypothesis tests and estimation for most one change point in the linear structural error-in-variables model. In the last, we use the method given by Lajors Horvath estimate the change point of Yen-Dollar exchange rates series.更多还原