不同数据下半变系数模型的统计分析
【摘要】 半变系数模型,又称为半参数变系数部分线性模型,是由Fan&Zhang(2002)在检验变系数模型的系数函数是否真正变化时提出来的一个新模型。它涵盖了许多通常的参数、非参数以及半参数回归模型。由于该模型不但结合了线性模型易于解释的优点以及非参数模型稳健的特性,而且能动态地描述协变量与响应变量之间的关系,同时也避免了许多“维数祸根”问题,所以,这个模型自提出以来就得到了很多的关注和研究,并广泛应用于工业、农业、金融、地理等领域。在经典的回归模型中,一般假定所得到的数据都是完全的、可靠的,并且误差项是相互独立的。而在实际应用中,由于人为或者系统的原因,这个假定是很难满足的,至少度量误差总是存在的。所以,研究存在度量误差的半变系数模型就更具有实际意义。为此,本文先讨论了完全数据下误差独立与误差相关的半变系数模型的统计推断问题,然后系统研究了协变量X与Z同时存在加性度量误差的半变系数模型的估计问题。本文主要结果之一是对完全数据下的半变系数模型分误差独立和误差相关进行了讨论,得到了相应的估计方法和处理办法。主要结果之二是研究了协变量X与Z同时存在度量误差的半变系数模型的估计问题,提出了一种基于核函数法的非参数部分的估计方法以及参数部分的估计,并证明了估计的相合性。主要结果之三是针对不同数据集下的半变系数模型所得的不同估计方法进行了数值模拟,探讨了方法的有效性。
硕士论文代写-【Abstract】 Semivarying coefficient model, which is also called as semiparametric varying-coefficient partially linear model,was first introduced by Fang and Zhang(2002) to test whether the coefficient functions of the varying coefficient model will truly change.It includes many usual parametric, nonparametric and semiparametric regression models.The new model have the merits of the linear model which are prone to easily interpretation and can display robust virtue as for nonparametric models.Besides, it can dynamically describe the relation between the covariates and the response variates and also can avoid many "curse of dimensionality" problems.Therefore, this model has received much attention since its birth, and it has been widely applied in industry, agriculture, finance, geography and some other fields.In the context of classic regression models, we generally assume that the sample data are complete, reliable, and the errors are mutually independent. But in many applications,the assumptions are hard to satisfy because of the nature of measurement mechanism or man-made factor. At least, there // always exist measurement errors.So it is more practical to investigate the semivarying coefficient errors-in-variables model.In this paper, first, we discussed the statistical inference of semivarying coefficient model with complete data, then we systematically investigated the estimation procedure of this model for their parametric and nonparametric varying-coefficient part under the case where the covariates are measured with additive errors.One of the main results of the paper was that we discussed the statistical inference of semivarying coefficient model with the independent or the correlated random errors.The second result was that we proposed a new method to estimate the parameters and coefficient functions of the semivarying coefficient errors-in-variables model based on the kernel estimation.The last result was that we did a numerical simulation to test the efficiency of the estimators of the semivarying coefficient model with different data sets.
【关键词】 半变系数模型； 度量误差； 剖面(profile)最小二乘估计； 核估计； 广义最小二乘法；
【Key words】 semivarying coefficient models； errors-in-variables； profile least square estimation； kernel estimation； the generalized least square method；