线性过程误差方差的相合估计  

Consistent Variance Estimate of Linear Process Errors

作　　者：武新乾[1] 程芳[1] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471023

出　　处：《河南大学学报（自然科学版）》2015年第4期399-403,共5页Journal of Henan University:Natural Science

基　　金：国家自然科学基金资助项目(11326181);河南省国际科技合作计划项目(134300510034);河南科技大学博士科研启动基金(09001322)

摘　　要：对于固定设计和线性过程误差下的非参数回归模型,为了估计误差方差,首先基于多项式样条方法给出了回归函数的估计,然后根据所得残差序列构造了误差方差的点估计,在没有混合相依的一般条件下证明了该估计的相合性.此外,还通过算例进行了数值模拟,结果显示,该估计方法可行,同时在误差方差估计的绝对误差意义下,自动选择结点的BIC准则优于AIC准则,基于BIC准则选择结点的样条方法还优于基于交错鉴定法选择带宽的局部线性方法.Nonparametric regression models with fixed design and linear process errors are considered. In order to define an estimate of error variance, the estimate of regression function is first given on the basis of polynomial spline method. Based on residual sequence, the point estimate of error variance is constructed. Consistency of the estimator is proved under some general conditions without mixing sequence. Furthermore, a numerical simulation example is given. The results show that the estimation is feasible. In the sense of the absolute error, BIC criterion, which is used to select knot number automatically, is superior to AIC criterion. Meanwhile, the spline method with selecting knot number through BIC criterion is also superior to the local linear method with cross validation band width choice.

关 键 词：非参数回归 线性过程 误差方差 多项式样条 

分 类 号：O212.7[理学—概率论与数理统计]