部分线性回归模型参数的差分k-d估计

发布时间：2018-01-02 18:09

本文关键词：部分线性回归模型参数的差分k-d估计　出处：《湖北师范大学》2016年硕士论文　论文类型：学位论文

【摘要】：1986年Engle et al在研究天气变化与供电需求之间的关系时第一次提出部分线性回归模型,这是非常重要的统计模型,考虑部分线性回归模型,其中观测值Xy,已知,参数?未知,f为未知的光滑函数,?为随机误差(?独立同分布).从提出部分线性回归模型之后,有关模型中参数?的研究一直是统计学中的热点问题.基于差分的方法,可消除数据对函数f的依赖,消除在部分线性回归模型中非线性部分的影响,因此不要求估计非线性部分,故通常称为差分方法.差分之后,部分线性回归模型就转化为类似于线性模型的形式,对于设计矩阵常常存在多重复共线性的情况,为了得到更高精度的参数估计,本文提出了部分线性回归模型中参数的差分k-d估计.第二章,定义部分线性回归模型中参数?的差分k-d估计之后,给出了该估计量的一些性质,并且证明在均方误差?MSE?和均方误差矩阵?MMSE?意义下,差分k-d估计优于Tabakan和Akdeniz(2010)提出的部分线性模型的差分岭估计.第三章,讨论了差分k-d估计中参数k和d估计量的选取问题及其分布.第四章,分别给出了模拟和实际应用,说明了本文的主要结论及该估计的优越性.
[Abstract]:In 1986 Engle et al during the study of the relationship between climate change and power supply when the demand is put forward for the first time partial linear regression model, it is very important to consider the statistical model, partial linear regression model, the observations of Xy, known as f unknown parameters?, smoothing function, unknown random error (?? IID). After this part of the linear regression model, the relevant parameters in the model? Research has been a hot issue in statistics. The method based on difference, can eliminate the data to the F function dependency, eliminate the nonlinear part influence on the part of the linear regression model, it does not require the estimation of nonlinear part, so commonly known method for the poor the difference after the partial linear regression model is transformed into linear model similar to the form of collinearity often exist for the design matrix, in order to get more accurate parameters estimation, the This paper presents estimates of the parameters in the model of linear regression of the differential k-d. In the second chapter, the definition of some parameters in the model are linear regression? The difference after the k-d estimation, gives some properties of this estimator, and prove that the mean square error and mean square error? MSE? Matrix? MMSE? Meaning, difference k-d estimation is better than that of Tabakan and Akdeniz (2010) estimators in partially linear model is proposed for the differential ridge. The third chapter discusses the difference in k-d estimation of parameters K and D to estimate the amount of selection and distribution. In the fourth chapter, the simulation and practical application are given, the main conclusions of this paper and the superiority the estimated.

【学位授予单位】：湖北师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.1

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