Abstract
In this paper, considering the nonparametric regression model $Y_{ni}=g(t_{i})+\varepsilon_{i}$ ( $1\leq i\leq n$ ), where $\varepsilon_{i}=\sum_{j=-\infty}^{\infty}a_{j}e_{i-j}$ and $e_{i-j}$ are identically distributed and ρ-mixing sequences. This paper obtains the Berry-Esseen bounds of the wavelet estimator of $g(\cdot)$ , the rates of the normal approximation are shown as $O(n^{-1/6})$ under certain conditions.
Highlights
The Berry-Esseen theorem of probability distribution concerns mainly research of statistics convergence to a certain distribution and the measure of the probability distributions of the statistics which determines the distribution as regards the absolute distance that can be controlled as an optimal problem.In recent years, the Berry-Esseen bounds theorem has got extensive investigation
Xue [ ] discussed the Berry-Esseen bound of an estimator for the variance in a semi-parametric regression model under some mild conditions, Liang and Li [ ] studied the asymptotic normality and the Berry-Esseen type bound of the estimator with linear process error, Li et al [ ] derived the Berry-Esseen bounds of the wavelet estimator for a nonparametric regression model with linear process errors generated by φ-mixing sequences, Li et al [ ] investigated the Berry-Esseen bounds of the wavelet estimator in a semi-parametric regression model with linear process errors
It is well known that a regression function estimation is an important method in data analysis and has a wide range of applications in filtering and prediction in communication and control systems, pattern recognition and classification, and econometrics
Summary
The Berry-Esseen theorem of probability distribution concerns mainly research of statistics convergence to a certain distribution and the measure of the probability distributions of the statistics which determines the distribution as regards the absolute distance that can be controlled as an optimal problem.In recent years, the Berry-Esseen bounds theorem has got extensive investigation. Where Fba := σ {{Xi : a ≤ i ≤ b}}, L (Fba) is the set of square integrable random variables on the condition of Fba. Definition . A sequence of random variables {Xi : i = , , .
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