Sequential profile Lasso for ultra-high-dimensional partially linear models
In this paper, we study ultra-high-dimensional partially linear models when the dimension of the linear predictors grows exponentially with the sample size. For the variable screening, we propose a sequential profile Lasso method (SPLasso) and show that it possesses the screening property. SPLasso c...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2017-07-01
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| Series: | Statistical Theory and Related Fields |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/24754269.2017.1396432 |
| _version_ | 1797677075693305856 |
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| author | Yujie Li Gaorong Li Tiejun Tong |
| author_facet | Yujie Li Gaorong Li Tiejun Tong |
| author_sort | Yujie Li |
| collection | DOAJ |
| description | In this paper, we study ultra-high-dimensional partially linear models when the dimension of the linear predictors grows exponentially with the sample size. For the variable screening, we propose a sequential profile Lasso method (SPLasso) and show that it possesses the screening property. SPLasso can also detect all relevant predictors with probability tending to one, no matter whether the ultra-high models involve both parametric and nonparametric parts. To select the best subset among the models generated by SPLasso, we propose an extended Bayesian information criterion (EBIC) for choosing the final model. We also conduct simulation studies and apply a real data example to assess the performance of the proposed method and compare with the existing method. |
| first_indexed | 2024-03-11T22:39:47Z |
| format | Article |
| id | doaj.art-5658481b0df34e07a3eea0ad9bca51d3 |
| institution | Directory Open Access Journal |
| issn | 2475-4269 2475-4277 |
| language | English |
| last_indexed | 2024-03-11T22:39:47Z |
| publishDate | 2017-07-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Statistical Theory and Related Fields |
| spelling | doaj.art-5658481b0df34e07a3eea0ad9bca51d32023-09-22T09:19:44ZengTaylor & Francis GroupStatistical Theory and Related Fields2475-42692475-42772017-07-011223424510.1080/24754269.2017.13964321396432Sequential profile Lasso for ultra-high-dimensional partially linear modelsYujie Li0Gaorong Li1Tiejun Tong2Beijing University of TechnologyBeijing Institute for Scientific and Engineering Computing, Beijing University of TechnologyHong Kong Baptist UniversityIn this paper, we study ultra-high-dimensional partially linear models when the dimension of the linear predictors grows exponentially with the sample size. For the variable screening, we propose a sequential profile Lasso method (SPLasso) and show that it possesses the screening property. SPLasso can also detect all relevant predictors with probability tending to one, no matter whether the ultra-high models involve both parametric and nonparametric parts. To select the best subset among the models generated by SPLasso, we propose an extended Bayesian information criterion (EBIC) for choosing the final model. We also conduct simulation studies and apply a real data example to assess the performance of the proposed method and compare with the existing method.http://dx.doi.org/10.1080/24754269.2017.1396432sequential profile lassopartially linear modelextended bayesian information criterionscreening propertyultra-high-dimensional data |
| spellingShingle | Yujie Li Gaorong Li Tiejun Tong Sequential profile Lasso for ultra-high-dimensional partially linear models Statistical Theory and Related Fields sequential profile lasso partially linear model extended bayesian information criterion screening property ultra-high-dimensional data |
| title | Sequential profile Lasso for ultra-high-dimensional partially linear models |
| title_full | Sequential profile Lasso for ultra-high-dimensional partially linear models |
| title_fullStr | Sequential profile Lasso for ultra-high-dimensional partially linear models |
| title_full_unstemmed | Sequential profile Lasso for ultra-high-dimensional partially linear models |
| title_short | Sequential profile Lasso for ultra-high-dimensional partially linear models |
| title_sort | sequential profile lasso for ultra high dimensional partially linear models |
| topic | sequential profile lasso partially linear model extended bayesian information criterion screening property ultra-high-dimensional data |
| url | http://dx.doi.org/10.1080/24754269.2017.1396432 |
| work_keys_str_mv | AT yujieli sequentialprofilelassoforultrahighdimensionalpartiallylinearmodels AT gaorongli sequentialprofilelassoforultrahighdimensionalpartiallylinearmodels AT tiejuntong sequentialprofilelassoforultrahighdimensionalpartiallylinearmodels |