泊松过程参数变点的统计推断

发布时间：2018-04-16 02:24

本文选题：泊松过程 + 变点　；参考：《新疆师范大学》2017年硕士论文

【摘要】：由于变点研究理论在各领域的广泛应用,对该问题的研究也成为了统计学研究的热门分支.泊松过程作为重要的随机过程之一,将变点研究方法应用于该过程,可以作为深入研究泊松过程的手段.因此对泊松过程参数的变点进行了统计推断研究.本文总共分为四章.第一章主要介绍了变点问题的学术背景,综述了变点问题的国内外文献及泊松过程的简单介绍.主要的研究内容在第二章与第三章,其中第二章主要研究了CUSUM型统计量在泊松过程参数变点问题的应用,得出如下两个结论:(1).σ2已知时,应用CUSUM统计量构造了本节的检验统计量Tk,对泊松过程参数变点进行了统计推断,求解了其拒绝域,在此基础上证明了变点估计的强相合性.(2).σ2未知时,利用正则思想找出了σ2的估计,从而建立了本节的检验统计量,得到了拒绝域,并给出变点位置的点估计.第三章应用U统计量构造适应于泊松过程的统计量Uk,在一定条件下讨论了该过程参数变点的假设检验问题,最后给出了变点位置的点估计值.
[Abstract]:Due to the wide application of change point theory in various fields, research on this problem has also become a hot research branch of statistics. The Poisson process as one of the most important stochastic process, will become the application of research methods in the research process, can be used as a Poisson process deeply. So the change point means the Poisson process parameters are discussed based on statistical inference. This paper is divided into four chapters. The first chapter mainly introduces the change point of the academic background, briefly reviewed the literature at home and abroad and the change point of the Poisson process. The main research contents in the second chapter and the third chapter, the second chapter mainly studies the application of CUSUM type statistic change point in the Poisson process parameters, draw the following two conclusions: (1). 2 sigma is known, was constructed using CUSUM statistic test statistic Tk of this section, the Poisson process parameter change point of statistical inference, solving The rejection regions, then prove the strong consistency of change point estimator. (2). 2 sigma is unknown, the use of regular thought out 2 sigma estimation, so as to establish the test statistic of this section, has been refused domain, and gives the location of change point estimation. In the third chapter, the application of U the statistic structure adapted to the Poisson process statistics Uk, hypothesis testing is the process parameter change point are discussed under certain conditions, finally gives the location of change point point estimates.

【学位授予单位】：新疆师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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