部分线性回归模型的估计

【作者】 白美利；

【导师】 郭鹏江；

【作者基本信息】 西北大学 ， 应用数学， 2010， 硕士

【摘要】 部分线性回归模型由于兼具参数部分和非参数部分,比较容易解释各个变量的影响情况,从而在实际应用中有着更强的灵活性和适用性。从1986年Engle等在研究电力需求和气候变化之间的关系时建立该模型,至今,国内外学者对部分线性回归模型的研究已具有相当的规模。在现有文献资料的基础上,本文就部分线性回归模型在误差为相依的情形下,运用一般权函数法并综合最小二乘法得到了未知参数和未知函数的估计量,接着讨论了估计量的相合性及渐近正态性。首先,本文对部分线性回归模型的历史背景及国内外的研究发展状况作以简介。主要是在观察值为固定设计时,对部分线性回归模型的误差项作各种不同假设,以便寻求对参数部分及非参数部分合理的估计方法及对所得估计量的大样本性质的讨论途径。其次,对部分线性回归模型在误差为线性过程时,利用两阶段估计法并综合一般权函数法及最小二乘法,得到了β和g(·)的估计量,然后利用鞅差序列加权和的中心极限定理,讨论了估计量的渐近正态性,进而证明了估计量的相合性。相比现有文献中关于估计量的相关性质的证明,本文的证明方法假设条件较弱,主要是去掉了一些跟对数运算有关的限制条件,引进了关于权函数的部分极限性质,使得条件更具有普遍性,也很容易验证,从而更便于操作和运用。最后,对上述模型在误差为ρ混合序列情形下,利用小波方法得到β和g(·)的估计量,进而证明了估计量的r-阶相合性。更多还原

【Abstract】 Including parametric component and non-paramertic component, partially linear regression models allow easier interpretation of the effect on each variable, so they are more flexible and universal than the classic linear models or non-paramertic regression models. Engle, Grabger, Rice and Weiss were among the first to consider the partially linear regression models. In 1986, they analyzed the ralationship between temperature and electricity usage. From then on, there have been maken great progress in the studies on partially linear models. In this paper, the consistency and asymptotic normality of the estimators are studied on the base of domestic and overseas scholar researches.Firstly, the partially linear regression models are introduced from the origin to the development at home and abroad, mainly including all kinds of estimation methods to parametric component and non-parametric component and studies to the properties of large sample. The studies are based on the different supposes to the errors in the models with fixed designed points.Secondly, considering the partially linear models with linear process errors Bying least squares and usual weighted function method combining two-stage estimation, we define the estimatorsβand g forβand g(·), then we obtain their r-order mean consistency, complete consistency and asymptotic normality under suitable conditions. Since given conditions become weaker, the means in this paper are more universal and flexible than other methods, there we remove some restrictions on logrithm calculation, and introduce some Iimite properties on power function.Finally, to the above model withρ-mixing sequence, we use Wavelet methods and obtain the estimators of/βand g(·), then we study the r-order consistency of the estimators.更多还原