鞅差误差下非参数方差模型的样条估计  

Spline Estimation for Nonparametric Variance Models Under Martingale Difference Errors

作　　者：武新乾[1] 梅倩倩[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：《河南科技大学学报（自然科学版）》2013年第2期91-94,1,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：河南省科技发展规划基金项目(092300410178);河南省教育厅自然科学研究计划基金项目(2010B110009;2008A110005);河南科技大学博士科研启动基金项目(09001322)

摘　　要：考虑固定设计和鞅差误差下的非参数方差模型,利用多项式样条方法,得到了非参数方差函数估计的最优全局收敛速度和一致收敛速度。模拟算例不仅说明了样条估计方法的可行性,而且其拟合效果和估计性质在一定条件下还优于局部线性方法。Nonparametric variance models with fixed design and martingale difference errors were considered in this paper.Based on polynomial spline method,consistent results for the estimator of variance function were discussed.Optimal global rate of convergence and uniform rate of convergence were obtained.Also,the feasibility of the spline estimation was illustrated by a simulation example.The results shows that the spline method outperforms the local linear method on the behavior of fitness and unbiased estimate under certain circumstances.

关 键 词：方差函数 样条 鞅差 收敛速度 

分 类 号：O212.7[理学—概率论与数理统计]