The Berry–Esseen type bounds of the weighted estimator in a nonparametric model with linear process errors

Xin Deng, Xuejun Wang () and Yi Wu
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Xin Deng: Chuzhou University
Xuejun Wang: Anhui University
Yi Wu: Anhui University

Statistical Papers, 2021, vol. 62, issue 2, No 17, 963-984

Abstract: Abstract In this paper, the Berry–Esseen type bounds of the weighted estimator in a nonparametric regression model are investigated under some mild conditions when random errors are from a linear process generated by $$\varphi $$ φ -mixing random variables. In particular, the rate of uniform normal approximation is near to $$O(n^{-\frac{3}{16}})$$ O ( n - 3 16 ) by the choice of some constants, which generalizes and improves the corresponding results of Li et al. (Stat Probab Lett 81:103–110, 2011) and Ding et al. (J Inequal Appl 2018:10, 2018). Finally, the simulation study is provided to verify the validity of the theoretical results.

Keywords: Weighted estimator; Berry–Esseen bound; Linear process; $$\varphi $$ φ -mixing random variables; 62G20; 62G08 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-019-01120-z

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