带有误差变量的自回归模型的局部多项式估计

数学物理学报 ›› 2010, Vol. 30 ›› Issue (4): 984-999.

带有误差变量的自回归模型的局部多项式估计

于卓熙^1,2, 王德辉¹, 史宁中³

1.吉林大学数学学院长春 130012||2.长春税务学院应用数学系长春 130117|3.东北师范大学长春 130021

收稿日期:2007-12-28 修回日期:2009-11-20 出版日期:2010-07-25 发布日期:2010-07-25
基金资助:
:国家自然科学基金(10971081, J0630104)、新世纪优秀人才支持计划(NCET-08-237)、高等学校博士学科点专项基金(20070183023)、吉林大学基本科研业务费(200810024)、吉林省教育厅``十一五''科学技术研究项目(2009514)和
长春税务学院科学研究项目(2008016)资助

Local Polynomial Estimator of the Regression Function in Autoregressive Models with Errors in Variables

YU Zhuo-Xi^1,2, WANG De-Hui¹, SHI Ning-Zhong³

1.College of Mathematics, Jilin University, Changchun 130012;
2.Department of Applied Mathematics, Changchun Taxation College, Changchun 130117;
3.Northeast Normal University, Changchun 130021

Received:2007-12-28 Revised:2009-11-20 Online:2010-07-25 Published:2010-07-25
Supported by:
:国家自然科学基金(10971081, J0630104)、新世纪优秀人才支持计划(NCET-08-237)、高等学校博士学科点专项基金(20070183023)、吉林大学基本科研业务费(200810024)、吉林省教育厅``十一五''科学技术研究项目(2009514)和
长春税务学院科学研究项目(2008016)资助

摘要/Abstract

摘要：

该文主要研究带有误差变量的自回归模型的自回归函数的非参数估计问题, 应用卷积核函数, 给出了自回归函数的局部多项式估计, 考察了局部多项式估计的相合性和渐近正态性, 最后作了模拟计算.

关键词: 带有误差变量的自回归模型, 卷积核函数, 局部多项式估计

Abstract:

In this paper, the authors study the problem of nonparametric estimation of the autoregression function in autoregressive models with errors-in-variables. With the application of the deconvolution kernel, the local polynomial estimator of the autoregression function is given. Under some specific conditions, the properties of consistency and asymptotic normality of the estimator can be obtained here. The performance of the method is studied by some simulation experiments.

Key words: Autoregressive models with errors-in-variables, Deconvolution kernel, Local polynomial estimator

中图分类号:

62M10

于卓熙, 王德辉, 史宁中. 带有误差变量的自回归模型的局部多项式估计[J]. 数学物理学报, 2010, 30(4): 984-999.

YU Zhuo-Xi, WANG De-Hui, SHI Ning-Zhong. Local Polynomial Estimator of the Regression Function in Autoregressive Models with Errors in Variables[J]. Acta mathematica scientia,Series A, 2010, 30(4): 984-999.

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