Abstract
Consider the following nonparametric model: \(Y_{ni}=g(x_{ni})+ \varepsilon _{ni},1\le i\le n,\) where \(x_{ni}\in {\mathbb {A}}\) are the nonrandom design points and \({\mathbb {A}}\) is a compact set of \({\mathbb {R}}^{m}\) for some \(m\ge 1\), \(g(\cdot )\) is a real valued function defined on \({\mathbb {A}}\), and \(\varepsilon _{n1},\ldots ,\varepsilon _{nn}\) are \(\rho ^{-}\)-mixing random errors with zero mean and finite variance. We obtain the Berry–Esseen bounds of the weighted estimator of \(g(\cdot )\). The rate can achieve nearly \(O(n^{-1/4})\) when the moment condition is appropriate. Moreover, we carry out some simulations to verify the validity of our results.
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The authors are most grateful to the Chief Editor, Associate Editor and two anonymous reviewers for carefully reading the manuscript and for valuable suggestions which helped in improving an earlier version of this paper.
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Supported by the National Natural Science Foundation of China (11671012, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1508085J06) and the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005).
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Wang, X., Wu, Y. & Hu, S. The Berry–Esseen bounds of the weighted estimator in a nonparametric regression model. Ann Inst Stat Math 71, 1143–1162 (2019). https://doi.org/10.1007/s10463-018-0677-6
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DOI: https://doi.org/10.1007/s10463-018-0677-6