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 |
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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 |
| _version_ | 1811203208409776128 |
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| author | Liwang Ding Yongming Li |
| author_facet | Liwang Ding Yongming Li |
| author_sort | Liwang Ding |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T02:51:59Z |
| format | Article |
| id | doaj.art-89947846810e4891a1742aa8342d33b3 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-12T02:51:59Z |
| publishDate | 2016-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-89947846810e4891a1742aa8342d33b32022-12-22T03:50:57ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-03-012016111210.1186/s13660-016-1036-xThe Berry-Esseen bounds of wavelet estimator for regression model whose errors form a linear process with a ρ-mixingLiwang Ding0Yongming Li1School of Information and Statistics, Guangxi University of Finance and EconomicsSchool of Mathematics and Computer Science, Shangrao Normal UniversityAbstract 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.http://link.springer.com/article/10.1186/s13660-016-1036-xwavelet estimatorρ-mixingBerry-Esseen boundlinear process |
| spellingShingle | Liwang Ding Yongming Li The Berry-Esseen bounds of wavelet estimator for regression model whose errors form a linear process with a ρ-mixing Journal of Inequalities and Applications wavelet estimator ρ-mixing Berry-Esseen bound linear process |
| title | The Berry-Esseen bounds of wavelet estimator for regression model whose errors form a linear process with a ρ-mixing |
| title_full | The Berry-Esseen bounds of wavelet estimator for regression model whose errors form a linear process with a ρ-mixing |
| title_fullStr | The Berry-Esseen bounds of wavelet estimator for regression model whose errors form a linear process with a ρ-mixing |
| title_full_unstemmed | The Berry-Esseen bounds of wavelet estimator for regression model whose errors form a linear process with a ρ-mixing |
| title_short | The Berry-Esseen bounds of wavelet estimator for regression model whose errors form a linear process with a ρ-mixing |
| title_sort | berry esseen bounds of wavelet estimator for regression model whose errors form a linear process with a ρ mixing |
| topic | wavelet estimator ρ-mixing Berry-Esseen bound linear process |
| url | http://link.springer.com/article/10.1186/s13660-016-1036-x |
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