The paper studies a partially linear regression model given by yi=xiTβ+f(ti)+εi,i=1,2,…,n,\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} y_i=x_i^T\beta +f(t_i)+\varepsilon _i,i=1,2,\ldots ,n, \end{aligned}$$\end{document}where {εi,i=1,2,…,n}\documentclass[12pt]{minimal}
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\begin{document}$$\{\varepsilon _i,i=1,2,\ldots , n\}$$\end{document} are independent and identically distributed random errors with zero mean and finite variance σ2>0\documentclass[12pt]{minimal}
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\begin{document}$$\sigma ^2>0$$\end{document}. Using a difference based and the Huber–Dutter (DHD) approaches, the estimators of unknown parametric component β\documentclass[12pt]{minimal}
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\begin{document}$$\beta $$\end{document} and root variance σ\documentclass[12pt]{minimal}
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\begin{document}$$\sigma $$\end{document} are given, and then the estimation of nonparametric component f(·)\documentclass[12pt]{minimal}
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\begin{document}$$f(\cdot )$$\end{document} is given by the wavelet method. The asymptotic normality of the DHD estimators of β\documentclass[12pt]{minimal}
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\begin{document}$$\beta $$\end{document} and σ\documentclass[12pt]{minimal}
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\begin{document}$$\sigma $$\end{document} are investigated, and the weak convergence rate of the estimator of f(·)\documentclass[12pt]{minimal}
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\begin{document}$$f(\cdot )$$\end{document} is also investigated. In addition, for stationary m\documentclass[12pt]{minimal}
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\begin{document}$$m$$\end{document}-dependent sequence of random variables, the central limit theorem is also obtained. At last, two examples are presented to illustrate the proposed method.
