The Berry-Esseen bound of a wavelet estimator in non-randomly designed nonparametric regression model based on ANA errors
ESAIM: Probability and Statistics, Tome 24 (2020), pp. 21-38

Consider the nonparametric regression model Y$$ = g(t$$) + ε$$, i = 1, 2, …, n,  n ≥ 1, where ε$$,  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.

DOI : 10.1051/ps/2019017
Classification : 62E20, 62G05
Keywords: Nonparametric regression model, asymptotically negatively associated random variables, wavelet estimator, Berry-Esseen bound 
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     author = {Tang, Xufei and Wang, Xuejun and Wu, Yi and Zhang, Fei},
     title = {The {Berry-Esseen} bound of a wavelet estimator in non-randomly designed nonparametric regression model based on {ANA} errors},
     journal = {ESAIM: Probability and Statistics},
     pages = {21--38},
     year = {2020},
     publisher = {EDP Sciences},
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     doi = {10.1051/ps/2019017},
     mrnumber = {4053000},
     zbl = {1440.62072},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps/2019017/}
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Tang, Xufei; Wang, Xuejun; Wu, Yi; Zhang, Fei. The Berry-Esseen bound of a wavelet estimator in non-randomly designed nonparametric regression model based on ANA errors. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 21-38. doi: 10.1051/ps/2019017

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Cité par Sources :

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).