A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression
Interest in variance estimation in nonparametric regression has grown greatly in the past several decades. Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement. Nevertheless, their method only appli...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/585146 |
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| _version_ | 1841524743772045312 |
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| author | Yuejin Zhou Yebin Cheng Tiejun Tong |
| author_facet | Yuejin Zhou Yebin Cheng Tiejun Tong |
| author_sort | Yuejin Zhou |
| collection | DOAJ |
| description | Interest in variance estimation in nonparametric regression has grown greatly in the past several decades. Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement. Nevertheless, their method only applies to regression models with homoscedastic errors. In this paper, we propose two least squares estimators for the error variance in heteroscedastic nonparametric regression: the intercept estimator and the slope estimator. Both estimators are shown to be consistent and their asymptotic properties are investigated. Finally, we demonstrate through simulation studies that the proposed estimators perform better than the existing competitor in various settings. |
| format | Article |
| id | doaj-art-bb313832067549d5ad4d17103daaef29 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-bb313832067549d5ad4d17103daaef292025-02-03T05:47:29ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/585146585146A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric RegressionYuejin Zhou0Yebin Cheng1Tiejun Tong2School of Science, Anhui University of Science and Technology, Huainan 232001, ChinaSchool of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 20043, ChinaDepartment of Mathematics, Hong Kong Baptist University, Hong KongInterest in variance estimation in nonparametric regression has grown greatly in the past several decades. Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement. Nevertheless, their method only applies to regression models with homoscedastic errors. In this paper, we propose two least squares estimators for the error variance in heteroscedastic nonparametric regression: the intercept estimator and the slope estimator. Both estimators are shown to be consistent and their asymptotic properties are investigated. Finally, we demonstrate through simulation studies that the proposed estimators perform better than the existing competitor in various settings.http://dx.doi.org/10.1155/2014/585146 |
| spellingShingle | Yuejin Zhou Yebin Cheng Tiejun Tong A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression Journal of Applied Mathematics |
| title | A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression |
| title_full | A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression |
| title_fullStr | A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression |
| title_full_unstemmed | A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression |
| title_short | A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression |
| title_sort | least squares method for variance estimation in heteroscedastic nonparametric regression |
| url | http://dx.doi.org/10.1155/2014/585146 |
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