位置参数变点的统计推断研究
发布时间：2019-05-22 19:38
【摘要】：变点问题自上世纪70年代以来一直是统计中的一个热门话题,它广泛应用于工业质量控制(最早产生变点问题统计研究的领域之一)、经济、生物统计、金融等各个领域。本论文基于反对称函数,应用CUSUM方法,探讨了位置参数变点估计量的统计性质。共分四章分别进行介绍：第一章首先简要概述了变点问题的由来、常见的研究方法以及变点问题的研究总结；其次,着重介绍了位置参数变点模型的研究现状以及U-统计量法在变点统计推断问题中的应用；再次,阐述了变点统计推断中渐近分布的研究现状；最后,简单说明了本论文的主要研究内容和研究结果。第二章针对至多一个位置参数变点的模型,应用累积和(CUSUM)方法给出了位置参数变点的U-统计量型估计量,并研究了变化度为常数时变点估计的相合性和收敛速度。进一步在局部对立假设条件下(θ=θn→0,n→∞),变点估计的相合性和收敛速度。第三章对位置参数变点模型进行了模拟分析,分析结果得出我们所给估计量的有效性。第四章给出了本文的研究的概括总结以及对变点问题发展的一些展望。
[Abstract]:The problem of variable point has been a hot topic in statistics since 1970s. It has been widely used in industrial quality control (one of the earliest fields of statistical research of variable point problem), economy, biostatistics, finance and so on. In this paper, based on the antisymmetric function and CUSUM method, the statistical properties of the variable point estimation of position parameters are discussed. It is divided into four chapters: the first chapter briefly summarizes the origin of the variable point problem, the common research methods and the research summary of the variable point problem. Secondly, the research status of position parameter variable point model and the application of U-statistics method in variable point statistical inference are introduced emphatically. thirdly, the research status of asymptotic distribution in variable point statistical inference is expounded. Finally, the main research contents and results of this paper are briefly explained. In chapter 2, for the model of more than one variable point of position parameter, the U-statistical type estimation of variable point of position parameter is given by using cumulative sum (CUSUM) method, and the consistency and convergence rate of the estimation of time-varying point with constant degree of change are studied. Furthermore, the consistency and convergence rate of variable point estimation are obtained under the assumption of local opposites (theta = theta n 鈮，
本文编号：2483197
[Abstract]:The problem of variable point has been a hot topic in statistics since 1970s. It has been widely used in industrial quality control (one of the earliest fields of statistical research of variable point problem), economy, biostatistics, finance and so on. In this paper, based on the antisymmetric function and CUSUM method, the statistical properties of the variable point estimation of position parameters are discussed. It is divided into four chapters: the first chapter briefly summarizes the origin of the variable point problem, the common research methods and the research summary of the variable point problem. Secondly, the research status of position parameter variable point model and the application of U-statistics method in variable point statistical inference are introduced emphatically. thirdly, the research status of asymptotic distribution in variable point statistical inference is expounded. Finally, the main research contents and results of this paper are briefly explained. In chapter 2, for the model of more than one variable point of position parameter, the U-statistical type estimation of variable point of position parameter is given by using cumulative sum (CUSUM) method, and the consistency and convergence rate of the estimation of time-varying point with constant degree of change are studied. Furthermore, the consistency and convergence rate of variable point estimation are obtained under the assumption of local opposites (theta = theta n 鈮，
本文编号：2483197
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