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Original Article

Berry–Esseen bound of wavelet estimators in heteroscedastic regression model with random errors

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Pages 821-852 | Received 08 Jan 2018, Accepted 06 Jun 2018, Published online: 18 Jul 2018
 

ABSTRACT

For the heteroscedastic regression model Yi=xiβ+g(ti)+σiei, 1in, where σi2=f(ui), (xi,ti,ui) are known to be nonrandom design points, g() and f() are defined on the closed interval [0,1]. When f() is known, we investigate the Berry–Esseen type bounds for wavelet estimators of β and g() under {ei} are identically distributed ϕ-mixing random errors, when f() is unknown, the Berry–Esseen type bounds for wavelet estimators of β, g() and f() established under {ei} are independent random errors.

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Additional information

Funding

This research is supported by the National Natural Science Foundation of China [11271189,11461057], National Science Foundation of Jiangxi Province [20161BAB201003], 2017 youth teacher research and development fund project of Guangxi University of Finance and Economics [2017QNA01].

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