| Issue |
ESAIM: PS
Volume 24, 2020
|
|
|---|---|---|
| Page(s) | 21 - 38 | |
| DOI | https://doi.org/10.1051/ps/2019017 | |
| Published online | 20 January 2020 | |
The Berry-Esseen bound of a wavelet estimator in non-randomly designed nonparametric regression model based on ANA errors*
1
School of Mathematics and Statistics, Chaohu University,
Hefei
238000, PR China.
2
School of Mathematical Sciences, Anhui University,
Hefei
230601, PR China.
** Corresponding author: wxjahdx2000@126.com
Received:
21
September
2018
Accepted:
13
July
2019
Consider the nonparametric regression model Yni = g(tni) + εi, i = 1, 2, …, n, n ≥ 1, where εi, 1 ≤ i ≤ n, are asymptotically negatively associated (ANA, for short) random variables. Under some appropriate conditions, the Berry-Esseen bound of the wavelet estimator of g(⋅) is established. In addition, some numerical simulations are provided in this paper. The results obtained in this paper generalize some corresponding ones in the literature.
Mathematics Subject Classification: 62E20 / 62G05
Key words: Nonparametric regression model / asymptotically negatively associated random variables / wavelet estimator / Berry-Esseen bound
Supported by the National Natural Science Foundation of China (11671012, 11871072, 11701004, 11701005), the Natural Science Foundation of Anhui Province (1808085QA03, 1908085QA01, 1908085QA07), the Research Project of Chaohu University (XLZ-201903, XLY-201905) and the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province (2017H123).
© EDP Sciences, SMAI 2020
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