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  

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

作　　者：李永明[1] 庞伟才 李乃医 Li Yongming;Pang Weicai;Li Naiyi(School of Mathematics and Computer Science,Jiangxi Shangrao Normal University,Jiangxi Shangrao 334001;School of Mathematics and Statistics,Nanning Normal University,Nanning 530001;School of Mathematics and Computer,Guangdong Ocean University,Guangdong Zhanjiang 524088)

机构地区：[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

出　　处：《数学物理学报（A辑）》2023年第5期1519-1528,共10页Acta Mathematica Scientia

基　　金：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)。

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.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^(−1/6)).The obtained results generalize the corresponding results in recent literature.

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 

分 类 号：O212.7[理学—概率论与数理统计]