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Teor. Veroyatnost. i Primenen., 2018, Volume 63, Issue 3, Pages 584–608 (Mi tvp5197)  

The Berry–Esseen bound for $\rho$-mixing random variables and its applications in nonparametric regression model

X. J. Wang, S. H. Hu

School of Mathematical Sciences, Anhui University, Hefei 230601, P. R. China

Abstract: In this paper, the Berry–Esseen bound for $\rho$-mixing random variables with the rate of normal approximation $O(n^{-1/6}\log n)$ is established under some suitable conditions. By using the Berry–Esseen bound, we further investigate the Berry–Esseen bound of sample quantiles for $\rho$-mixing random variables. The rate of normal approximation is shown to be $O(n^{-1/6}\log n)$ under some suitable conditions. In addition, the asymptotic normality of the linear weighted estimator for the nonparametric regression model based on $\rho$-mixing errors is studied by using the Berry–Esseen bound that we established. Some new results are obtained in the paper under much weaker dependent structures.

Keywords: Berry–Esseen bound, normal approximation, nonparametric regression model, sample quantiles, $\rho$-mixing sequence.

Funding Agency Grant Number
National Natural Science Foundation of China 11671012
11501004
11501005
Natural Science Foundation of Anhui Province 1508085J06
Key Projects for Academic Talent of Anhui Province gxbjZD2016005
Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province 2017H123
Supported by the National Natural Science Foundation of China (11671012, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1508085J06), the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005) and the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province (2017H123).


DOI: https://doi.org/10.4213/tvp5197

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English version:
Theory of Probability and its Applications, 2019, 63:3, 479–499

Bibliographic databases:

Received: 12.06.2016
Revised: 14.12.2017
Accepted:05.04.2018
Language:

Citation: X. J. Wang, S. H. Hu, “The Berry–Esseen bound for $\rho$-mixing random variables and its applications in nonparametric regression model”, Teor. Veroyatnost. i Primenen., 63:3 (2018), 584–608; Theory Probab. Appl., 63:3 (2019), 479–499

Citation in format AMSBIB
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\paper The Berry--Esseen bound for $\rho$-mixing random variables and its applications in nonparametric regression model
\jour Teor. Veroyatnost. i Primenen.
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\vol 63
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\pages 584--608
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\crossref{https://doi.org/10.4213/tvp5197}
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\pages 479--499
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