位置參數(shù)變點的統(tǒng)計推斷研究
發(fā)布時間：2019-05-22 19:38
【摘要】：變點問題自上世紀(jì)70年代以來一直是統(tǒng)計中的一個熱門話題,它廣泛應(yīng)用于工業(yè)質(zhì)量控制(最早產(chǎn)生變點問題統(tǒng)計研究的領(lǐng)域之一)、經(jīng)濟(jì)、生物統(tǒng)計、金融等各個領(lǐng)域。本論文基于反對稱函數(shù),應(yīng)用CUSUM方法,探討了位置參數(shù)變點估計量的統(tǒng)計性質(zhì)。共分四章分別進(jìn)行介紹：第一章首先簡要概述了變點問題的由來、常見的研究方法以及變點問題的研究總結(jié)；其次,著重介紹了位置參數(shù)變點模型的研究現(xiàn)狀以及U-統(tǒng)計量法在變點統(tǒng)計推斷問題中的應(yīng)用；再次,闡述了變點統(tǒng)計推斷中漸近分布的研究現(xiàn)狀；最后,簡單說明了本論文的主要研究內(nèi)容和研究結(jié)果。第二章針對至多一個位置參數(shù)變點的模型,應(yīng)用累積和(CUSUM)方法給出了位置參數(shù)變點的U-統(tǒng)計量型估計量,并研究了變化度為常數(shù)時變點估計的相合性和收斂速度。進(jìn)一步在局部對立假設(shè)條件下(θ=θn→0,n→∞),變點估計的相合性和收斂速度。第三章對位置參數(shù)變點模型進(jìn)行了模擬分析,分析結(jié)果得出我們所給估計量的有效性。第四章給出了本文的研究的概括總結(jié)以及對變點問題發(fā)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，
本文編號：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，
本文編號：2483197
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