本文選題：泊松過程 + 變點(diǎn)��； 參考：《新疆師范大學(xué)》2017年碩士論文

【摘要】：由于變點(diǎn)研究理論在各領(lǐng)域的廣泛應(yīng)用,對該問題的研究也成為了統(tǒng)計(jì)學(xué)研究的熱門分支.泊松過程作為重要的隨機(jī)過程之一,將變點(diǎn)研究方法應(yīng)用于該過程,可以作為深入研究泊松過程的手段.因此對泊松過程參數(shù)的變點(diǎn)進(jìn)行了統(tǒng)計(jì)推斷研究.本文總共分為四章.第一章主要介紹了變點(diǎn)問題的學(xué)術(shù)背景,綜述了變點(diǎn)問題的國內(nèi)外文獻(xiàn)及泊松過程的簡單介紹.主要的研究內(nèi)容在第二章與第三章,其中第二章主要研究了CUSUM型統(tǒng)計(jì)量在泊松過程參數(shù)變點(diǎn)問題的應(yīng)用,得出如下兩個(gè)結(jié)論:(1).σ2已知時(shí),應(yīng)用CUSUM統(tǒng)計(jì)量構(gòu)造了本節(jié)的檢驗(yàn)統(tǒng)計(jì)量Tk,對泊松過程參數(shù)變點(diǎn)進(jìn)行了統(tǒng)計(jì)推斷,求解了其拒絕域,在此基礎(chǔ)上證明了變點(diǎn)估計(jì)的強(qiáng)相合性.(2).σ2未知時(shí),利用正則思想找出了σ2的估計(jì),從而建立了本節(jié)的檢驗(yàn)統(tǒng)計(jì)量,得到了拒絕域,并給出變點(diǎn)位置的點(diǎn)估計(jì).第三章應(yīng)用U統(tǒng)計(jì)量構(gòu)造適應(yīng)于泊松過程的統(tǒng)計(jì)量Uk,在一定條件下討論了該過程參數(shù)變點(diǎn)的假設(shè)檢驗(yàn)問題,最后給出了變點(diǎn)位置的點(diǎn)估計(jì)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.

【學(xué)位授予單位】：新疆師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.1

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