The Berry-Esseen bounds of wavelet estimator for regression model whose errors form a linear process with a ρ-mixing
Abstract In this paper, considering the nonparametric regression model Y n i = g ( t i ) + ε i $Y_{ni}=g(t_{i})+\varepsilon_{i}$ ( 1 ≤ i ≤ n $1\leq i\leq n$ ), where ε i = ∑ j = − ∞ ∞ a j e i − j $\varepsilon_{i}=\sum_{j=-\infty}^{\infty}a_{j}e_{i-j}$ and e i − j $e_{i-j}$ are identically distribute...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2016-03-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1036-x |
| Summary: | Abstract In this paper, considering the nonparametric regression model Y n i = g ( t i ) + ε i $Y_{ni}=g(t_{i})+\varepsilon_{i}$ ( 1 ≤ i ≤ n $1\leq i\leq n$ ), where ε i = ∑ j = − ∞ ∞ a j e i − j $\varepsilon_{i}=\sum_{j=-\infty}^{\infty}a_{j}e_{i-j}$ and e i − j $e_{i-j}$ are identically distributed and ρ-mixing sequences. This paper obtains the Berry-Esseen bounds of the wavelet estimator of g ( ⋅ ) $g(\cdot)$ , the rates of the normal approximation are shown as O ( n − 1 / 6 ) $O(n^{-1/6})$ under certain conditions. |
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| ISSN: | 1029-242X |