Consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors
Abstract In this paper, we establish the strong consistency and complete consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors under some general conditions. We also obtain the rates of strong consistency and complete consistency. We show...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-03-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-019-2016-8 |
| _version_ | 1828894922874290176 |
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| author | Qihui He |
| author_facet | Qihui He |
| author_sort | Qihui He |
| collection | DOAJ |
| description | Abstract In this paper, we establish the strong consistency and complete consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors under some general conditions. We also obtain the rates of strong consistency and complete consistency. We show that the rates can approximate to O(n−1/3) $O(n^{-1/3})$ under appropriate conditions. The results obtained in the paper improve or extend the corresponding ones to widely orthant dependent assumptions. |
| first_indexed | 2024-12-13T14:20:11Z |
| format | Article |
| id | doaj.art-bc69e48e58494ae2b4e8d51f9f5435c5 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-13T14:20:11Z |
| publishDate | 2019-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-bc69e48e58494ae2b4e8d51f9f5435c52022-12-21T23:42:07ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-03-012019111310.1186/s13660-019-2016-8Consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errorsQihui He0Department of Foundational Teaching, Anhui Institute of Economic ManagementAbstract In this paper, we establish the strong consistency and complete consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors under some general conditions. We also obtain the rates of strong consistency and complete consistency. We show that the rates can approximate to O(n−1/3) $O(n^{-1/3})$ under appropriate conditions. The results obtained in the paper improve or extend the corresponding ones to widely orthant dependent assumptions.http://link.springer.com/article/10.1186/s13660-019-2016-8Strong consistencyComplete consistencyRateNonparametric regression modelWidely orthant dependent |
| spellingShingle | Qihui He Consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors Journal of Inequalities and Applications Strong consistency Complete consistency Rate Nonparametric regression model Widely orthant dependent |
| title | Consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors |
| title_full | Consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors |
| title_fullStr | Consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors |
| title_full_unstemmed | Consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors |
| title_short | Consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors |
| title_sort | consistency of the priestley chao estimator in nonparametric regression model with widely orthant dependent errors |
| topic | Strong consistency Complete consistency Rate Nonparametric regression model Widely orthant dependent |
| url | http://link.springer.com/article/10.1186/s13660-019-2016-8 |
| work_keys_str_mv | AT qihuihe consistencyofthepriestleychaoestimatorinnonparametricregressionmodelwithwidelyorthantdependenterrors |