基于LENQD序列生成的线性过程误差回归函数小波估计Berry-Esseen界

数学物理学报 ›› 2023, Vol. 43 ›› Issue (5): 1519-1528.

基于LENQD序列生成的线性过程误差回归函数小波估计Berry-Esseen界

李永明^1,^*(),庞伟才²(),李乃医³()

¹上饶师范学院数学与计算机科学学院江西上饶 334001
²南宁师范大学数学与统计学院南宁 530001
³广东海洋大学数学与计算机学院广东湛江 524088

收稿日期:2022-06-06 修回日期:2023-01-12 出版日期:2023-10-26 发布日期:2023-08-09
通讯作者: 李永明 E-mail:lym1019@163.com;pangweicai2021@163.com;linaiyi1979@163.com
作者简介:庞伟才，Email: pangweicai2021@163.com;|李乃医，Email:linaiyi1979@163.com
基金资助:
国家自然科学基金项目(12161074);江西省自然科学基金重点项目(20212ACB201006);广东省自然科学基金项目(2022A1515010978);上饶市科技计划(2020K006)

Berry-Esseen Bound of Wavelet Estimator for Regression Model with Linear Process Errors Generated by LENQD Sequence

Li Yongming^1,^*(),Pang Weicai²(),Li Naiyi³()

¹School of Mathematics and Computer Science, Jiangxi Shangrao Normal University, Jiangxi Shangrao 334001
²School of Mathematics and Statistics, Nanning Normal University, Nanning 530001
³School of Mathematics and Computer, Guangdong Ocean University, Guangdong Zhanjiang 524088

Received:2022-06-06 Revised:2023-01-12 Online:2023-10-26 Published:2023-08-09
Contact: Yongming Li E-mail:lym1019@163.com;pangweicai2021@163.com;linaiyi1979@163.com
Supported by:
NSFC(12161074);NSFJ(20212ACB201006);NSFG(2022A1515010978);Shangrao Science and Technology Talent Plan(2020K006)

摘要/Abstract

摘要：

在LENQD相依序列生产的线性过程误差下, 研究了固定设计非参数回归模型小波估计. 利用LENQD序列的矩不等式和特征函数不等式, 建立了未知回归函数小波估计的Berry-Esseen界. 通过选取适当的参数, 其界可达$O(n^{-1/6})$. 所得结果推广了相关文献的研究结果.

关键词: 固定设计回归模型, 线性过程, LENQD序列, 小波估计, Berry-Esseen界

Abstract:

Based on linear process random errors generated by LENQD random sequence, the wavelet estimator of nonparametric fixed design regression model is considered. By the characteristic function inequality and moment inequality of LENQD random sequence, the Berry-Esseen bounds of the wavelet estimator for unknown regression function are obtained. And by choosing some suitable constants, their bounds can reach $O(n^{-\frac{1}{6}})$. The obtained results generalize the corresponding results in recent literature.

Key words: Fixed design regression, Linear process, LENQD random sequence, Wavelet estimator, Berry-Esseen bound

中图分类号:

O212.7

李永明,庞伟才,李乃医. 基于LENQD序列生成的线性过程误差回归函数小波估计Berry-Esseen界[J]. 数学物理学报, 2023, 43(5): 1519-1528.

Li Yongming,Pang Weicai,Li Naiyi. Berry-Esseen Bound of Wavelet Estimator for Regression Model with Linear Process Errors Generated by LENQD Sequence[J]. Acta mathematica scientia,Series A, 2023, 43(5): 1519-1528.

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