M-estimation in high-dimensional linear model
Abstract We mainly study the M-estimation method for the high-dimensional linear regression model and discuss the properties of the M-estimator when the penalty term is a local linear approximation. In fact, the M-estimation method is a framework which covers the methods of the least absolute deviat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-08-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1819-3 |
| _version_ | 1811323018150936576 |
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| author | Kai Wang Yanling Zhu |
| author_facet | Kai Wang Yanling Zhu |
| author_sort | Kai Wang |
| collection | DOAJ |
| description | Abstract We mainly study the M-estimation method for the high-dimensional linear regression model and discuss the properties of the M-estimator when the penalty term is a local linear approximation. In fact, the M-estimation method is a framework which covers the methods of the least absolute deviation, the quantile regression, the least squares regression and the Huber regression. We show that the proposed estimator possesses the good properties by applying certain assumptions. In the part of the numerical simulation, we select the appropriate algorithm to show the good robustness of this method. |
| first_indexed | 2024-04-13T13:46:36Z |
| format | Article |
| id | doaj.art-5404678a747a4af6b31d2195ddd8a982 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-13T13:46:36Z |
| publishDate | 2018-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-5404678a747a4af6b31d2195ddd8a9822022-12-22T02:44:28ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-08-012018111310.1186/s13660-018-1819-3M-estimation in high-dimensional linear modelKai Wang0Yanling Zhu1School of Statistics and Applied Mathematics, Anhui University of Finance and EconomicsSchool of Statistics and Applied Mathematics, Anhui University of Finance and EconomicsAbstract We mainly study the M-estimation method for the high-dimensional linear regression model and discuss the properties of the M-estimator when the penalty term is a local linear approximation. In fact, the M-estimation method is a framework which covers the methods of the least absolute deviation, the quantile regression, the least squares regression and the Huber regression. We show that the proposed estimator possesses the good properties by applying certain assumptions. In the part of the numerical simulation, we select the appropriate algorithm to show the good robustness of this method.http://link.springer.com/article/10.1186/s13660-018-1819-3M-estimationHigh-dimensionalityVariable selectionOracle propertyPenalized method |
| spellingShingle | Kai Wang Yanling Zhu M-estimation in high-dimensional linear model Journal of Inequalities and Applications M-estimation High-dimensionality Variable selection Oracle property Penalized method |
| title | M-estimation in high-dimensional linear model |
| title_full | M-estimation in high-dimensional linear model |
| title_fullStr | M-estimation in high-dimensional linear model |
| title_full_unstemmed | M-estimation in high-dimensional linear model |
| title_short | M-estimation in high-dimensional linear model |
| title_sort | m estimation in high dimensional linear model |
| topic | M-estimation High-dimensionality Variable selection Oracle property Penalized method |
| url | http://link.springer.com/article/10.1186/s13660-018-1819-3 |
| work_keys_str_mv | AT kaiwang mestimationinhighdimensionallinearmodel AT yanlingzhu mestimationinhighdimensionallinearmodel |