本文關(guān)鍵詞： 方差變點 非參數(shù)回歸 變點估計 檢驗統(tǒng)計量　出處：《西安科技大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：目前時間序列分析中變點問題的研究是統(tǒng)計學(xué)研究里一類熱門問題,也一直備受國內(nèi)外眾多學(xué)者的關(guān)注。以往的變點研究主要集中在均值發(fā)生變化的情況,如今對方差變點的研究正處在炙熱時期。本文首先介紹了變點的相關(guān)背景和研究意義,以及非參數(shù)回歸較參數(shù)回歸的優(yōu)勢。另外在已有的變點理論和方法的基礎(chǔ)上,用非參數(shù)方法對兩種情形的時間序列方差變點進行了研究。第一種情形是針對獨立隨機變量單方差變點的研究:針對獨立序列均值變點的研究,局部思想法體現(xiàn)出很好的檢驗估計效果,本文在此基礎(chǔ)上用局部思想法和滑窗法的結(jié)合對獨立隨機變量序列中存在方差變點的問題進行研究,并給出了變點的檢驗統(tǒng)計量和變點的估計,以及檢驗統(tǒng)計量的極限分布,理論證明了此情形下方差變點估計的強相合性和強收斂速度,并用實驗數(shù)值模擬驗證了此方法的有效性。第二種情形是針對隨機設(shè)計下非參數(shù)回歸模型方差變點的研究:利用局部線性核估計來擬合回歸曲線,并構(gòu)造殘差序列及CUSUM檢驗統(tǒng)計量,在一定假設(shè)條件下推導(dǎo)證明了檢驗統(tǒng)計量的漸近分布,驗證了檢驗統(tǒng)計量收斂于Brown橋的上確界,并利用不同的核函數(shù)估計驗證了局部線性核估計對核函數(shù)的選取影響不大,最后用實驗數(shù)值模擬驗證了局部線性核估計較其他核估計存在邊界效應(yīng)的問題明顯減弱,這樣既改進又拓展了原有的方法。最后對本文做了總結(jié),并提出進一步需要研究的問題。
[Abstract]:At present, the study of change point problem in time series analysis is a kind of popular problem in statistical research, and has been concerned by many scholars both at home and abroad. In the past, the study of change point mainly focused on the change of mean value. At present, the study of the variation point is in a hot period. This paper first introduces the background and significance of the change point, as well as the advantage of non-parametric regression over parametric regression. In addition, on the basis of the existing theory and method of change point, The nonparametric method is used to study the variance variability of time series in two cases. The first case is the single variance change point of independent random variable, the other is the change point of the mean value of independent sequence. The local thought method shows a good effect of test estimation. Based on this, the problem of variance variation point in independent random variable sequence is studied by the combination of local thinking method and sliding window method. The test statistics, the estimates of the change points and the limit distribution of the test statistics are given. The strong consistency and the strong convergence rate of the variance change point estimators are proved theoretically. The effectiveness of the method is verified by experimental numerical simulation. The second case is the study of variance change point of nonparametric regression model under random design: local linear kernel estimation is used to fit the regression curve. The asymptotic distribution of test statistics is proved under certain assumptions, and the convergence of test statistics to the upper bound of Brown bridge is verified. The local linear kernel estimation has little effect on the selection of kernel function by using different kernel function estimators. Finally, the problem of boundary effect between local linear kernel estimators and other kernel estimators is obviously weakened by experimental numerical simulation. This not only improves the original method, but also extends the original method. Finally, the paper summarizes the paper and puts forward some problems that need further study.
【學(xué)位授予單位】：西安科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O212.1

【參考文獻】

相關(guān)期刊論文 前1條

1 陳希孺;INFERENCE IN A SIMPLE CHANGE-POINT MODEL[J];Science in China,Ser.A;1988年06期

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本文編號：1499459