本文選題：線性回歸模型 + NSD隨機(jī)序列��； 參考：《湖北師范大學(xué)》2017年碩士論文

【摘要】：線性回歸模型是當(dāng)今統(tǒng)計(jì)模型中應(yīng)用最基本最廣泛的一種模型,在工程技術(shù)、經(jīng)濟(jì)學(xué)和社會(huì)科學(xué)中具有很大的應(yīng)用價(jià)值.然而,一些傳統(tǒng)的參數(shù)估計(jì)方法,如最小二乘法缺乏穩(wěn)健性.1964年Huber提出克服這一缺陷的M估計(jì)(參考文獻(xiàn)Huber[1]),此后,M估計(jì)便受到統(tǒng)計(jì)學(xué)者的廣泛關(guān)注與深入研究.很多回歸模型問題的研究中,常常假定誤差是獨(dú)立同分布的隨機(jī)變量.然而Huber指出,獨(dú)立誤差的條件比較保守,并且在很多實(shí)際應(yīng)用中誤差常常表現(xiàn)出某種相依性,因此研究相依誤差的線性回歸模型具有很重要的理論與實(shí)際意義.負(fù)超可加相依(NSD)序列是一類較負(fù)相協(xié)(NA)序列更廣泛的序列,在介體理論和經(jīng)濟(jì)學(xué)中具有重要的應(yīng)用價(jià)值.因此本文研究誤差為NSD線性回歸模型M估計(jì)的漸近性質(zhì),主要內(nèi)容如下:第二章,在合適的條件下,采用隨機(jī)變量的截?cái)喾椒ń⒘薔SD隨機(jī)序列的中心極限定理和加權(quán)和中心極限定理.第三章,利用第二章中NSD隨機(jī)序列加權(quán)和的中心極限定理,證明了誤差為NSD的線性回歸模型(不含有常數(shù)項(xiàng)和含有常數(shù)項(xiàng))M估計(jì)的漸近正態(tài)性.第四章,考慮第三章提到的誤差為NSD序列的回歸模型,基于M準(zhǔn)則,提出了一個(gè)穩(wěn)健的M檢驗(yàn),并得到了M檢驗(yàn)統(tǒng)計(jì)量的漸近分布.第五章,通過蒙特卡羅模擬方法,借用R軟件對(duì)回歸參數(shù)進(jìn)行估計(jì),并且計(jì)算出M檢驗(yàn)的勢(shì),證明了M檢驗(yàn)統(tǒng)計(jì)量的漸近分布為2?分布.上述結(jié)論既推廣了Rao,Zhao[11]和Bai,Rao,Wu[12]對(duì)于誤差為獨(dú)立時(shí)線性回歸模型M估計(jì)漸近正態(tài)性的相應(yīng)結(jié)論,又推廣了Zhao,Chen[13]關(guān)于線性回歸模型M檢驗(yàn)統(tǒng)計(jì)量漸近分布的相應(yīng)結(jié)論,同時(shí)也推廣了陳希孺和趙林城[8]中線性回歸模型M估計(jì)的漸近理論.
[Abstract]:Linear regression model is one of the most basic and widely used models in current statistical models. It has great application value in engineering, economics and social sciences. However, some traditional parameter estimation methods, such as the least square method, lack robustness. In 1964, Huber proposed M estimation to overcome this defect (Huber [1]). Since then, M estimation has been widely concerned and deeply studied by statisticians. In many studies of regression model problems, the error is often assumed to be a random variable with independent and same distribution. However, Huber points out that the condition of independent error is conservative, and the error often shows some dependence in many practical applications. Therefore, it is of great theoretical and practical significance to study the linear regression model of dependent error. The negative superadditive dependent (NSD) sequence is a more extensive class of sequences than the negative associative NAN sequence, which has important application value in mediator theory and economics. Therefore, in this paper, we study the asymptotic properties of M-estimators for NSD linear regression models. The main contents are as follows: in Chapter 2, under suitable conditions, The central limit theorem and weighted sum central limit theorem of NSD random sequence are established by using the truncation method of random variables. In chapter 3, by using the central limit theorem of the weighted sum of NSD random sequences in chapter 2, we prove the asymptotic normality of linear regression models with errors of NSD. In chapter 4, considering that the error mentioned in chapter 3 is the regression model of NSD sequence, a robust M-test is proposed based on M criterion, and the asymptotic distribution of M-test statistics is obtained. In chapter 5, by using Monte Carlo simulation method, the regression parameters are estimated by using R software, and the potential of M test is calculated, and the asymptotic distribution of M test statistics is proved to be 2? Distribution. The above conclusions not only generalize the corresponding conclusions of Rao Zhao [11] and Baihu Rao Wu [12] for the asymptotic normality of M estimation of linear regression model when the error is independent, but also generalize the corresponding conclusion of Zhaojian Chen [13] on the asymptotic distribution of M test statistics in linear regression model. The asymptotic theory of M-estimators for linear regression models in Chen Xiru and Zhao Lincheng [8] is also generalized.
【學(xué)位授予單位】：湖北師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：C815

【參考文獻(xiàn)】

相關(guān)期刊論文 前4條

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本文編號(hào)：1948814