污染数据线性回归模型的统计推断
发布时间：2019-02-16 03:09
【摘要】：同删失数据一样,在实际工作中经常会遇到一些关于污染数据的统计分析问题.1952年Davis [1]首次提出污染数据和污染系数的概念.所谓的“污染”模型即为观察值的分布未知或至少部分观察值的分布未知的模型,并且它是由污染源的干扰所致,而这种污染源有别于模型本身,通过观察污染数据得到的(这些数据假设分布已知).1996年,郑祖康等提出了两类污染数据回归模型,并且在回归误差和污染源均服从正态分布假设条件下利用最小二乘法给出了模型参数和污染系数的估计.1998年,陈明华在去掉正态假设条件,利用最小二乘法给出了回归参数和污染系数的估计,并且证明了这些估计量的强相合性.本文的主要工作分为两个方面：首先,本文考虑污染数据的线性回归模型,在回归误差和污染源均服从Laplace分布下,给出了回归参数的最小一乘估计,并证明它的相合性和渐近正态性；同时使用模拟对估计方法的小样本性质进行了分析.模拟结果显示,本文所提方法在小样本情况下表现良好.其次,结合最小一乘估计和经验似然的思想得到回归参数的置信区间.
[Abstract]:Like censored data, we often encounter some problems of statistical analysis of pollution data in practice. In 1952, Davis [1] put forward the concept of pollution data and pollution coefficient for the first time. The so-called "pollution" model is a model in which the distribution of observed values is unknown, or at least part of the observed values are unknown, and it is caused by the interference of the source of pollution, which is different from the model itself. In 1996, Zheng Zukang and others put forward two kinds of regression models of pollution data. The model parameters and pollution coefficient are estimated by using the least square method under the assumption of regression error and pollution source from normal distribution. In 1998, Chen Minghua removed the normal assumption condition. The regression parameters and pollution coefficients are estimated by the least square method, and the strong consistency of these estimators is proved. The main work of this paper is divided into two aspects: firstly, considering the linear regression model of pollution data, under the Laplace distribution of regression error and pollution source, the least one multiplication estimate of regression parameters is given. Its consistency and asymptotic normality are proved. At the same time, the small sample properties of the estimation method are analyzed by simulation. The simulation results show that the proposed method performs well in the case of small samples. Secondly, the confidence interval of regression parameters is obtained by combining the least one multiplicative estimator and the idea of empirical likelihood.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1
本文编号：2423980
[Abstract]:Like censored data, we often encounter some problems of statistical analysis of pollution data in practice. In 1952, Davis [1] put forward the concept of pollution data and pollution coefficient for the first time. The so-called "pollution" model is a model in which the distribution of observed values is unknown, or at least part of the observed values are unknown, and it is caused by the interference of the source of pollution, which is different from the model itself. In 1996, Zheng Zukang and others put forward two kinds of regression models of pollution data. The model parameters and pollution coefficient are estimated by using the least square method under the assumption of regression error and pollution source from normal distribution. In 1998, Chen Minghua removed the normal assumption condition. The regression parameters and pollution coefficients are estimated by the least square method, and the strong consistency of these estimators is proved. The main work of this paper is divided into two aspects: firstly, considering the linear regression model of pollution data, under the Laplace distribution of regression error and pollution source, the least one multiplication estimate of regression parameters is given. Its consistency and asymptotic normality are proved. At the same time, the small sample properties of the estimation method are analyzed by simulation. The simulation results show that the proposed method performs well in the case of small samples. Secondly, the confidence interval of regression parameters is obtained by combining the least one multiplicative estimator and the idea of empirical likelihood.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1
【参考文献】
相关期刊论文 前6条
1 胡玉萍,王霞,李学相;污染数据回归分析参数的区间估计[J];郑州大学学报(工学版);2003年04期
2 钱伟民,翟健茹;污染数据线性回归模型的参数估计[J];同济大学学报(自然科学版);2003年02期
3 潘建敏;污染数据半参数回归模型的估计方法[J];工程数学学报;1997年03期
4 郑祖康,丁邦俊,杨瑛,殷弘;关于两类污染数据回归分析的参数估计[J];高校应用数学学报A辑(中文版);1996年01期
5 陈希孺,白志东,赵林城,吴月华;线性模型中最小一乘估计的渐近正态性[J];中国科学(A辑 数学 物理学 天文学 技术科学);1990年05期
6 郑祖康;A CLASS OF ESTIMATORS OF THE PARAMETERS IN LINEAR REGRESSION WITH CENSORED DATA[J];Acta Mathematicae Applicatae Sinica(English Series);1987年03期
，本文编号：2423980
本文链接：https://www.wllwen.com/kejilunwen/yysx/2423980.html
