缺失数据下带约束条件的部分线性变系数EV模型估计

发布时间：2018-05-25 08:10

本文选题：部分线性变系数EV模型 + 调整加权最小二乘估计　；参考：《兰州理工大学》2017年硕士论文

【摘要】：部分线性变系数模型是近年来提出的一个具有很强实际应用性的模型.该模型形式包含了很多子模型,例如参数、非参数以及半参数模型都可以看做为部分线性变系数模型的特例,所以其不但具有线性模型形式简单,易于观察的优点、非参数模型稳健的特征,还能够动态的表达协变量与相应变量之间的相互关系.通常在建立回归模型时,我们认为所得到的观测数据都是完整的,准确的,且误差项彼此相互独立并不考虑数据测量误差,或者缺失响应变量.但是在实际生产过程中,没有测量误差或者缺失响应变量的数据,通常很难得到,或者需要付出极大成本去提高精度.而在实际生产过程中,这都是不现实的.所以当研究回归模型时需要考虑到这些外部因素对模型的影响,然后再对模型的参数进行估计.第一章,主要介绍了本文所研究问题的背景、部分线性变系数EV模型的研究发展、现状以及本文研究所需的一些理论知识.第二章,考虑模型在带有测量误差及约束条件下情形下的回归情况.运用调整最小二乘估计和Lagrange乘数法估计未知参数和系数函数,在一定条件下证明参数、非参数函数估计的相合性,并模拟实验结果.第三章,研究了响应变量缺失下,参数具有线性约束且参数部分和非参数部分都带有测量误差的部分线性变系数模型的估计问题,利用最小二乘法和局部纠偏方法给出模型中参数和系数函数的估计,在一定的条件下证明了它们的渐近性质.
[Abstract]:Partial linear variable coefficient model is a model with strong practical application proposed in recent years. The model form contains many submodels, such as parametric, nonparametric and semi-parametric models, which can be regarded as special cases of partial linear variable coefficient models, so it not only has the advantages of simple form of linear model, but also easy to observe. The robust features of the nonparametric model can also dynamically express the relationship between the covariable and the corresponding variable. When we build the regression model, we think that the observed data are complete and accurate, and the error terms are independent of each other without considering the measurement error or the missing response variables. However, in the actual production process, the data without measurement errors or missing response variables are usually difficult to obtain, or need to pay a great deal of cost to improve the accuracy. In the actual production process, this is unrealistic. Therefore, when studying the regression model, we should consider the influence of these external factors on the model, and then estimate the parameters of the model. In the first chapter, we introduce the background of the problem, the research development of partial linear variable coefficient EV model, the present situation and some theoretical knowledge needed in this paper. In chapter 2, the regression of the model with measurement error and constraint is considered. By using the method of adjusted least square and Lagrange multiplier to estimate the unknown parameter and coefficient function, the consistency of parameter and nonparametric function estimation is proved under certain conditions, and the experimental results are simulated. In chapter 3, we study the estimation of partial linear variable coefficient model with linear constraints and measurement errors in both parametric and nonparametric parts under the absence of response variables. The estimation of the parameter and coefficient function in the model is given by using the least square method and the local correction method. Their asymptotic properties are proved under certain conditions.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

【参考文献】