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A Berry-Esseen type bound of wavelet estimator under linear process errors based on a strong mixing sequence. (English) Zbl 1279.62094
Summary: Consider the nonparametric regression model \(Y_{ni}=g(t_{ni}) + \varepsilon_{ni}, 1\leq i \leq n\), where \(\{t_{ni}\}\) are known design points, and the errors \(\{\varepsilon_{ni}\}\) have a linear representation \(\varepsilon_{ni}=\sum^\infty_{j=-\infty}a_je_{i-j}\) with \(\sum^\infty_{i=-\infty}|a_i|<\infty\) and \(\{e_i, -\infty<t<\infty\}\) are strong mixing random variables. \(g(\cdot)\) is an unknown function defined on closed interval \([0,1]\), which is estimated by a linear wavelet estimator \(\hat{g}_n(t)\). The main result of this article is that of providing, under certain regularity conditions, a Berry-Esseen bound for the linear wavelet estimator \(\hat{g}_n(t)\) which can attain \(O(n^{-1/6})\).
MSC:
62G08 Nonparametric regression and quantile regression
65T60 Numerical methods for wavelets
62G05 Nonparametric estimation
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