本文關鍵詞：多元正態(tài)向量均值變點在線監(jiān)測　出處：《山西大學》2015年碩士論文　論文類型：學位論文

  更多相關文章： 多元正態(tài)分布 變點監(jiān)測 殘差 遞歸殘差 平均運行長度 窗寬參數(shù)

【摘要】：變點問題是自上世紀70年代以來的熱門課題。最初應用在工業(yè)質(zhì)量控制中,后來又逐漸滲透到經(jīng)濟、金融、醫(yī)學、氣候分析等諸多領域。近三十年來,隨著統(tǒng)計學者在這一領域的投入,目前已有大量關于變點理論和應用方面的學術論文。已有論文中關于位置參數(shù)變點的研究有很多,尤其是關于均值變點的研究,而關于多元均值變點的研究則比較少。本文主要研究了正態(tài)多元向量均值變點監(jiān)測問題。文中我們利用殘差累積和與遞歸殘差累積和構造統(tǒng)計量,在原假設下得到了監(jiān)測統(tǒng)計量的漸近分布,在備擇假設下證明了該監(jiān)測統(tǒng)計量的一致性,并模擬得到統(tǒng)計量的臨界值。數(shù)字模擬實驗與生產(chǎn)實例表明,當變點的位置靠前時該統(tǒng)計量有較高的勢,但是當變點的位置靠后時并不總能及時監(jiān)測到變點。因此,我們采用引入窗寬參數(shù)的方法,對統(tǒng)計量進行修正,使得對位置靠后的變點能及時預警。模擬結果表明,引入窗寬參數(shù)確實能夠提高監(jiān)測統(tǒng)計量的勢,同時能減小平均運行長度。最后的生產(chǎn)實例也能說明該方法的實用性和有效性。
[Abstract]:The change point problem is a hot topic since the last century since 70s. The initial application in industrial quality control, then gradually penetrated into the economic, financial, medical, climate analysis and other areas. In the past thirty years, with statistical researchers in this field, there are a large amount of change point theory and Application the academic papers have studied in this thesis. A variable position parameters are many, especially the research on the mean change point, and the research on multivariate mean change point is relatively small. This paper mainly studies the normal vector of mean change point detection problem. In this paper, we make use of the residual accumulation and accumulation of recursive residuals and the structure of the statistic, under the null hypothesis and obtain the asymptotic distribution of the monitoring statistic, the consistency of the monitoring statistic is proved under the alternative hypothesis, and simulate the critical value of statistics. The digital simulation experiment with the students Production examples show that when the change point position in front of the statistics have high potential, but when the change point position back does not always detect the change point. Therefore, we proposed using window width parameter, to statistic correction, the change point position on the timely warning simulation. The results show that the bandwidth parameter can indeed improve the monitoring statistics, at the same time can reduce the average run length. The final production examples can illustrate the practicability and effectiveness of the method.

【學位授予單位】：山西大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O212.4

【共引文獻】

相關期刊論文 前2條

1 Weiqi LIU;Jinfang LIU;Ruibing QIN;;Monitoring Change in the Mean Vector of Multivariate Normal Distribution[J];Journal of Mathematical Research with Applications;2015年04期

2 劉維奇;劉晉芳;秦瑞兵;;多元正態(tài)向量變點在線監(jiān)測[J];山西大學學報(自然科學版);2015年03期

相關博士學位論文 前1條

1 張陽;內(nèi)生結構突變理論與應用研究[D];南開大學;2013年

相關碩士學位論文 前1條

1 朱華亮;跳躍度變點估計的統(tǒng)計推斷研究[D];合肥工業(yè)大學;2014年

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本文編號：1360836