Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (5): 1519-1528.

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

Li Yongming1,*(),Pang Weicai2(),Li Naiyi3()   

  1. 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)

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

CLC Number: 

  • O212.7
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