非参数回归模型基于残差的样条估计  

Spline Estimation Based on Residuals of Nonparametric Regression Model

作　　者：马晓跃 武新乾[1] MA Xiaoyue;WU Xinqian(Mathematics&Statistics School,Henan University of Science&Technology,Luoyang 471023,China)

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）》2021年第4期91-96,M0008,共7页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11601126);河南省重点攻关项目(182102210286)。

摘　　要：为了探究固定设计下具有α-混合相依误差的非参数回归模型的估计理论,基于多样式样条方法对均值函数进行了估计,利用残差构造了方差函数的样条估计。在一般假设条件下,均值函数估计量和方差函数估计量具有相同的一致收敛速度。数值模拟结果显示:基于贝叶斯信息准则下的样条估计优于赤池信息准则下的样条估计和局部线性估计。To explore the estimation theory of nonparametric regression models with fixed design andα-mixing dependent errors,the estimation of mean function on the basis of polynomial spline method and a spline estimation based on residuals of the variance function were constructed.Under general assumptions,both the estimators of mean function and variance function have the same uniform rate of convergence.Moreover,numerical simulation results show that the spline estimation based on Bayes information criterion outperforms the spline estimation based on Akaike information criterion and the local linear estimation.

关 键 词：非参数回归 样条估计 一致收敛速度 Α-混合 

分 类 号：O212.7[理学—概率论与数理统计]