NSD误差的线性模型M估计的渐近性质

发布时间：2018-05-29 00:38

本文选题：线性回归模型 + NSD随机序列　；参考：《湖北师范大学》2017年硕士论文

【摘要】：线性回归模型是当今统计模型中应用最基本最广泛的一种模型,在工程技术、经济学和社会科学中具有很大的应用价值.然而,一些传统的参数估计方法,如最小二乘法缺乏稳健性.1964年Huber提出克服这一缺陷的M估计(参考文献Huber[1]),此后,M估计便受到统计学者的广泛关注与深入研究.很多回归模型问题的研究中,常常假定误差是独立同分布的随机变量.然而Huber指出,独立误差的条件比较保守,并且在很多实际应用中误差常常表现出某种相依性,因此研究相依误差的线性回归模型具有很重要的理论与实际意义.负超可加相依(NSD)序列是一类较负相协(NA)序列更广泛的序列,在介体理论和经济学中具有重要的应用价值.因此本文研究误差为NSD线性回归模型M估计的渐近性质,主要内容如下:第二章,在合适的条件下,采用随机变量的截断方法建立了NSD随机序列的中心极限定理和加权和中心极限定理.第三章,利用第二章中NSD随机序列加权和的中心极限定理,证明了误差为NSD的线性回归模型(不含有常数项和含有常数项)M估计的渐近正态性.第四章,考虑第三章提到的误差为NSD序列的回归模型,基于M准则,提出了一个稳健的M检验,并得到了M检验统计量的渐近分布.第五章,通过蒙特卡罗模拟方法,借用R软件对回归参数进行估计,并且计算出M检验的势,证明了M检验统计量的渐近分布为2?分布.上述结论既推广了Rao,Zhao[11]和Bai,Rao,Wu[12]对于误差为独立时线性回归模型M估计渐近正态性的相应结论,又推广了Zhao,Chen[13]关于线性回归模型M检验统计量渐近分布的相应结论,同时也推广了陈希孺和赵林城[8]中线性回归模型M估计的渐近理论.
[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.
【学位授予单位】：湖北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C815

【参考文献】