半参数模型中有偏估计的进一步研究

发布时间：2018-06-19 06:09

本文选题：半参数模型 + 差分法　；参考：《重庆大学》2015年硕士论文

【摘要】：半参数线性回归模型中包含了参数部分(线性关系),也包含了非参数部分(非线性关系),因此半参数线性回归模型就同时具有了经典线性模型和非参数模型的优点,对实际问题的解释也更具有说服力,因此吸引了大量的学者进行研究,并被广泛的运用于经济、金融、生物、管理、医学、气象、工程技术、工农业和环境科学等各个领域。有大量的研究者对半参数模型进行了研究,得到了大量的研究成果,已经形成了一套比较完善成熟的理论系统。处理半参数线性模型的方法有很多,其中主要的有:补偿最小二乘法(广义最小二乘估计),两步估计,差分法,两阶段估计,稳健估计等等。但是在实际问题中广泛存在一种现象,即是存在复共线性,那么前面的估计方法在估计参数部分时用的最小二乘估计,得到的结果就不理想,甚至是错误的。在线性模型中,大量的学者研究了当设计矩阵是病态的情况,但是在半参数模型中,相关研究则较少。众所周知在经典线性模型中为了降低复共线性的不良影响,提出了有偏估计,其中重要的有偏估计有:Stein压缩估计,主成分估计,岭估计,minimax估计,Liu估计等。同样,在半参数模型中也可以引入相应的有偏估计来解决存在复共线性的情况。因此笔者在本文就做了以下几方面的工作:对于半参数线性回归模型,常用的主要方法有:补偿最小二乘法(广义最小二乘估计),两阶段估计,两步估计和稳健估计等等,但是在本文主要考虑的是用差分法来研究半参数线性回归模型,由于无偏性是参数估计的一个非常重要的优良的统计性质。因此本文提出了基于差分法的几乎无偏估计,包括基于差分法的几乎无偏岭估计和基于差分法的几乎无偏Liu估计。并证明了在MSE准则和偏差准则下,基于差分法的几乎无偏岭估计和基于差分法的几乎无偏Liu估计是优于基于差分法的岭估计和基于差分法的Liu估计以及最小二乘估计,最后利用R软件对其进行了随机模拟分析和实证分析验证。对于基于差分法的岭估计,其中有个非常值得研究的问题,就是岭参数的选取。在本文最后一部分,本文对岭参数的选取进行了随机模拟分析,得出了在不同的情况下,不同的岭参数估计方法的优良性。在实际应用中,给不同情况下的岭参数的估计方法的选择,提供了一个参考依据。
[Abstract]:The semi-parametric linear regression model contains both parametric part (linear relation) and nonparametric part (nonlinear relation), so the semi-parametric linear regression model has the advantages of both classical linear model and nonparametric model. The explanation of practical problems is also more persuasive, so it attracts a large number of scholars to study, and is widely used in economics, finance, biology, management, medicine, meteorology, engineering, agriculture and environmental science and other fields. A large number of researchers have studied the semi-parametric model, obtained a lot of research results, and formed a set of relatively mature theoretical system. There are many methods for dealing with semi-parametric linear models, among which the main ones are the compensated least squares method (generalized least squares estimation, two-step estimation, difference method, two-stage estimation, robust estimation, etc.) However, there is a phenomenon that there is complex collinearity in practical problems, so the least square estimation used in the estimation of parameters in the previous method is not ideal or even wrong. In the linear model, a large number of scholars have studied when the design matrix is ill-conditioned, but in the semi-parametric model, the related research is less. It is well known that in classical linear models, in order to reduce the adverse effects of complex collinearity, biased estimates are proposed, among which the important biased estimators are the: Stein contractive estimators, principal component estimators, ridge minimax estimators, Liu estimators, and so on. In the same way, the corresponding biased estimators can be introduced to solve the problem of complex collinearity in the semi-parametric model. Therefore, the author has done the following work in this paper: for the semi-parametric linear regression model, the main methods commonly used are: compensatory least square method (generalized least squares estimation, two-stage estimation, two-step estimation and robust estimation, etc.) However, the main consideration in this paper is to study the semi-parametric linear regression model by difference method. Unbiased property is a very important statistical property of parameter estimation. This paper presents almost unbiased estimates based on difference method, including almost unbiased ridge estimation based on difference method and almost unbiased Liu estimate based on difference method. It is proved that under MSE criterion and deviation criterion, almost unbiased ridge estimation based on difference method and almost unbiased Liu estimate based on difference method are superior to ridge estimation based on difference method, Liu estimate based on difference method and least square estimate. At last, the random simulation analysis and empirical analysis are carried out with R software. For the ridge estimation based on difference method, there is a problem that is worth studying, that is, the selection of ridge parameters. In the last part of this paper, the selection of ridge parameters is analyzed by random simulation, and the superiority of different ridge parameter estimation methods is obtained under different conditions. In practical application, a reference is provided for the selection of ridge parameter estimation methods under different conditions.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1

【相似文献】