强混合误差回归函数小波估计的Berry-Esseen界

数学物理学报 ›› 2009, Vol. 29 ›› Issue (5): 1453-1463.

• 论文 • 上一篇

强混合误差回归函数小波估计的Berry-Esseen界

1.上饶师范学院数学系江西上饶 334001；2.广西师范学院数学科学学院南宁 530023

收稿日期:2008-04-11 修回日期:2009-06-10 出版日期:2009-10-25 发布日期:2009-10-25
基金资助:
国家自然科学基金(10161004)、江西省自然科学基金(2008GZS0046)、江西省教育厅科技项目(GJJ09375)和广西自然科学基金 (0832108)资助

Berry-Esseen Bounds for Wavelet Estimator of Regression Function under Strong Mixing Process

1.Department of Mathematics, Shangrao Normal University, |jiangxi Shangrao 334001; 2.School of Mathematical Sciences, Guangxi Teachers Education University, Nanning 530023

Received:2008-04-11 Revised:2009-06-10 Online:2009-10-25 Published:2009-10-25

摘要/Abstract

摘要：

设回归模型 Y_ni=g(t_ni)+ε_ni, i =1, …, n, 其中{t_ni} 为固定设计点列, g(?) 是定义在[0,1]上的未知函数, {ε_ni}为随机误差. 该文主要讨论了误差为强混合序列情形下, 回归函数g(?)小波估计的Berry-Esseen 界, 其界可达 O(n-^1/6).

关键词: 小波估计, 固定设计回归模型, 强混合序列, Berry-Esseen界

Abstract:

Consider the nonparametric regression model Y_ni=g(t_ni)+ε_ni~ (i=1, …, n) with wavelet method, where the design points {t_ni} are known and nonrandom, g(?) is an unknown function defined on the closed interval [0,1], and {ε_ni} are strictly stationary strong mixing processes.
Under appropriate conditions, we derive Berry-Esseen bounds for wavelet estimator of g(?). As a corollary, we give the Berry-Esseen bounds that can attain O(n-^1/6).

Key words: Wavelet estimator, Fixed design regression, Strong mixing, Berry-Esseen bound

中图分类号:

62G05

李永明, 韦程东. 强混合误差回归函数小波估计的Berry-Esseen界[J]. 数学物理学报, 2009, 29(5): 1453-1463.

LI Yong-Ming, WEI Cheng-Dong. Berry-Esseen Bounds for Wavelet Estimator of Regression Function under Strong Mixing Process[J]. Acta mathematica scientia,Series A, 2009, 29(5): 1453-1463.

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强混合误差回归函数小波估计的Berry-Esseen界

Berry-Esseen Bounds for Wavelet Estimator of Regression Function under Strong Mixing Process

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