Consistency properties for the wavelet estimator in nonparametric regression model with dependent errors
Abstract In this paper, we establish the pth mean consistency, complete consistency, and the rate of complete consistency for the wavelet estimator in a nonparametric regression model with m-extended negatively dependent random errors. We show that the best rates can be nearly O ( n − 1 / 3 ) $O(n^{...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-09-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02603-0 |
| _version_ | 1831762751041568768 |
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| author | Qihui He Mingming Chen |
| author_facet | Qihui He Mingming Chen |
| author_sort | Qihui He |
| collection | DOAJ |
| description | Abstract In this paper, we establish the pth mean consistency, complete consistency, and the rate of complete consistency for the wavelet estimator in a nonparametric regression model with m-extended negatively dependent random errors. We show that the best rates can be nearly O ( n − 1 / 3 ) $O(n^{-1/3})$ under some general conditions. The results obtained in the paper markedly improve and extend some corresponding ones to a much more general setting. |
| first_indexed | 2024-12-22T05:13:47Z |
| format | Article |
| id | doaj.art-785c0538c9464e3481dd3ad63ce07090 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-22T05:13:47Z |
| publishDate | 2021-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-785c0538c9464e3481dd3ad63ce070902022-12-21T18:37:55ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-09-012021111510.1186/s13660-021-02603-0Consistency properties for the wavelet estimator in nonparametric regression model with dependent errorsQihui He0Mingming Chen1Department of Foundational Teaching, Anhui Academy of GovernanceDepartment of Foundational Teaching, Anhui Academy of GovernanceAbstract In this paper, we establish the pth mean consistency, complete consistency, and the rate of complete consistency for the wavelet estimator in a nonparametric regression model with m-extended negatively dependent random errors. We show that the best rates can be nearly O ( n − 1 / 3 ) $O(n^{-1/3})$ under some general conditions. The results obtained in the paper markedly improve and extend some corresponding ones to a much more general setting.https://doi.org/10.1186/s13660-021-02603-0Mean consistencyComplete consistencyRate of consistencyNonparametric regression modelm-extended negative dependence |
| spellingShingle | Qihui He Mingming Chen Consistency properties for the wavelet estimator in nonparametric regression model with dependent errors Journal of Inequalities and Applications Mean consistency Complete consistency Rate of consistency Nonparametric regression model m-extended negative dependence |
| title | Consistency properties for the wavelet estimator in nonparametric regression model with dependent errors |
| title_full | Consistency properties for the wavelet estimator in nonparametric regression model with dependent errors |
| title_fullStr | Consistency properties for the wavelet estimator in nonparametric regression model with dependent errors |
| title_full_unstemmed | Consistency properties for the wavelet estimator in nonparametric regression model with dependent errors |
| title_short | Consistency properties for the wavelet estimator in nonparametric regression model with dependent errors |
| title_sort | consistency properties for the wavelet estimator in nonparametric regression model with dependent errors |
| topic | Mean consistency Complete consistency Rate of consistency Nonparametric regression model m-extended negative dependence |
| url | https://doi.org/10.1186/s13660-021-02603-0 |
| work_keys_str_mv | AT qihuihe consistencypropertiesforthewaveletestimatorinnonparametricregressionmodelwithdependenterrors AT mingmingchen consistencypropertiesforthewaveletestimatorinnonparametricregressionmodelwithdependenterrors |