【作者】 曾秋芳；

【导师】 杨善朝；

【作者基本信息】 广西师范大学 ， 概率论与数理统计， 2012， 硕士

【摘要】 非参数回归估计是研究回归模型的一种有用工具,在金融经济方面有重要应用,如在金融资产价格和收益率波动性等方面有重要的的研究应用.在非参数回归估计中,通常采用权函数回归估计.自Sotne(1977)提出非参数回归估计的权函数估计方法后,其方法引起了广泛的重视.对于固定设计回归模型Yi=g(xi)+εi,1≤i≤n,Gass and Muller[1](1979)引入了权函数从而称为Gasser-Muller型权函数回归估计,其中K(·)是Borel可测函数,0<hn→0(当n→∞).自从Gasser and Miiller提出Gasser-Muller回归权估计后,相继有一些学者对Gasser-Muller回归权估计进行了研究.Roussas, G.G., Tran, L.T.and Ioannides,D.A[3](1992)在a混合序列下讨论了该估计的渐近正态性,但没有给出收敛速度.Jianqing Fan[4](1992)通过两个模型改变有限样本容量进行模拟,比较了Gasser-Muller权估计,Nadaraya-Watson回归权估计和局部线性回归估计三种估计的均方误差及线性光滑性.Xiaoling Dou and Shongo Shirahata[5](2009)采用Gasser-Muller回归权估计用于一些评价基准和进行设计程序编程的模拟,并得出Gasser-Muller回归权估计的模拟结果优于局部多项式估计.然而Gasser-Muller回归权估计的理论研究却比较少,因此,研究该估计不仅可以完善非参数回归的理论,还有着重要的现实意义.本文在在ρ混合序列和NOD序列情形下研究Gasser-Muller回归权估计的大样本性质,研究的主要内容和结果如下：首先,讨论在样本为ρ混合序列和NOD序列情形下Gasser-Muller回归权估计的强相合性,推广了文献[13]中的推论,并减弱了文献[7]结论的条件.其次,讨论在样本为ρ混合序列情形下Gasser-Muller回归权估计的一致渐近正态性,并给出一致渐近正态性的收敛速度,其收敛速度约为n-1/6.再次,对一些ρ混合序列和NOD序列的Gasser-Muller回归权估计进行数值模拟.由数值模拟结果发现,当样本容量越多时,估计的误差越小,精度越高.最后,选取我国股市的上证180和上证金融进行实证研究.更多还原

【Abstract】 The nonparametric regression estimation is a useful tool in researching regression model. It is applied widely in financial economics, such as financial asset price and volatility of return rate. In nonparametric regression estimation, the weighted estimator of regression function is always employed. Since Sotne (1977) proposed the weight function of estimation method which is belonged to nonparametric regression estimates, this method is caused a wide attention. For fixed design regression model Yi=g(xi)+εi,1≤i≤n, Gasser and Muller[1](1979) introduced the weight function is called as Gasser-Miiller type weight function regression estimation, where K(-) is Borel mea-surable function,0<hn→0(when n→∞). Since Gass and Muller put forward the Gasser-Miiller regression weighted right estimate, some scholars have studied it. Roussas G. G., Tran L. T. and Ioannides, D. A.[3](1992) discussed the asymptotic normality under the mixed sequence. But they didn’t provide the convergence rate. Jianqing Fan [4](1992) made the perform simula-tion through two model and changing sample size to compare the mean square error and linear smoothness of the Gasser-Miiller regression right estimate, Nadaraya-Watson regression weighted estimation and the local linear regression estimation. Xiaoling Dou and Shongo Shirahata [5](2009) made some evaluating criteria and some simulations of the programming design with the help of Gasser-Muller regression right evaluation. The simulation results show that the Gasser-Miiller regression weighted estimates is better the local polynomial estimates.However the theory of the Gasser-Muller regression weighted estimation is researched sel-dom. Therefore, to research its theory not only can improve the nonparametric regression theory but also has an important practical significance to research this estimates.In this paper, the author studies the large sample properties of the Gasser-Muller regression weighted estimate for the p mixed sequence and NOD sequence case. And the main research contents and the results are as follows:First of all, discuss the strong consistency of the Gasser-Muller regression right estimate of the strong consistency with the help of in the sample for p mixed sequence and NOD sequence case. extend the corollaries of theorems in literature[13] and weaken the conditions of the theorem in literature[7].Second, discuss the uniformly asymptotic normality of the Gasser-Muller regression weighted estimate for p mixed sequence case. And then provide the uniformly asymptotic normality con-vergence speed. Its convergence rate is about n-1/6.Third, do some numerical simulation for the p mixed sequence and NOD sequence. From the numerical simulation results, the author finds that when the sample size is more, the estimated error is smaller and the accuracy is higher.Finally, the author selects Shanghai Stock180index of Chinese stock market and the Shanghai Stock financial index to do empirical research.更多还原