系数函数光滑度互不相同的变系数模型的一步估计法

数学物理学报

系数函数光滑度互不相同的变系数模型的一步估计法

唐庆国; 王金德

(南京理工大学经济管理学院南京 210094; 解放军理工大学理学院南京 210007)

收稿日期:2006-07-18 修回日期:2007-12-04 出版日期:2008-08-25 发布日期:2008-08-25
通讯作者: 唐庆国
基金资助:
国家自然科学基金(10671089) 资助

One-step Estimation for Varying Coefficient Models with Unknown Functions of Different Degrees of Smoothness

Tang Qingguo; Wang Jinde

(School of Economics and Management, Nanjing University of Science and Technology, Nanjing 210094; Institute of Sciences, PLA University of Science and Technology, Nanjing 210007)

Received:2006-07-18 Revised:2007-12-04 Online:2008-08-25 Published:2008-08-25
Contact: Tang Qingguo

摘要/Abstract

摘要： 该文提出了一种一步估计方法用以估计变系数模型中具有互不相同光滑度的未知函数, 所有未知函数和它们的导数的估计量由一次极小化得到. 给出了估计量的渐近性质, 包括渐近偏差、方差和渐近分布, 一步估计量被证明达到了最优收敛速度.

关键词: 变系数模型, 互不相同光滑度, 一步估计法, 最优收敛速度

Abstract: An one-step estimation method is proposed to estimate all the unknown functions in varying coefficient models, of which the degrees of smoothness may be different from each other. In one-step estimation approach, the local estimators of all the unknown functions and their derivatives can be obtained by only one minimization operation. The asymptotic properties of the estimators, including bias, variance and asymptotic distribution, are derived. It is shown that all the one-step estimators achieve the optimal convergence rates.

Key words: Varying coefficient model, Different degrees of smoothness, One-step estimation, Optimal convergence rate

中图分类号:

62G07

唐庆国; 王金德. 系数函数光滑度互不相同的变系数模型的一步估计法[J]. 数学物理学报, 2008, 28(4): 701-710.

Tang Qingguo; Wang Jinde. One-step Estimation for Varying Coefficient Models with Unknown Functions of Different Degrees of Smoothness[J]. Acta mathematica scientia,Series A, 2008, 28(4): 701-710.

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