Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model
This paper focuses on a high-dimensional semi-parametric regression model in which a partially linear model is used for the parametric part and the B-spline basis function approach is used to estimate the unknown function for the non-parametric part. Within the framework of this model, the constrain...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/24/4767 |
| _version_ | 1797456445522837504 |
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| author | Aifen Feng Xiaogai Chang Youlin Shang Jingya Fan |
| author_facet | Aifen Feng Xiaogai Chang Youlin Shang Jingya Fan |
| author_sort | Aifen Feng |
| collection | DOAJ |
| description | This paper focuses on a high-dimensional semi-parametric regression model in which a partially linear model is used for the parametric part and the B-spline basis function approach is used to estimate the unknown function for the non-parametric part. Within the framework of this model, the constrained least squares estimation is investigated, and the alternating-direction multiplier method (ADMM) is used to solve the model. The convergence is proved under certain conditions. Finally, numerical simulations are performed and applied to workers’ wage data from CPS85. The results show that the ADMM algorithm is very effective in solving high-dimensional partially linear models. |
| first_indexed | 2024-03-09T16:07:55Z |
| format | Article |
| id | doaj.art-388b7c2095ca41cd91e77ca6b5d3d05b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:07:55Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-388b7c2095ca41cd91e77ca6b5d3d05b2023-11-24T16:29:22ZengMDPI AGMathematics2227-73902022-12-011024476710.3390/math10244767Application of the ADMM Algorithm for a High-Dimensional Partially Linear ModelAifen Feng0Xiaogai Chang1Youlin Shang2Jingya Fan3School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaThis paper focuses on a high-dimensional semi-parametric regression model in which a partially linear model is used for the parametric part and the B-spline basis function approach is used to estimate the unknown function for the non-parametric part. Within the framework of this model, the constrained least squares estimation is investigated, and the alternating-direction multiplier method (ADMM) is used to solve the model. The convergence is proved under certain conditions. Finally, numerical simulations are performed and applied to workers’ wage data from CPS85. The results show that the ADMM algorithm is very effective in solving high-dimensional partially linear models.https://www.mdpi.com/2227-7390/10/24/4767partially linear modelB-spline interpolationADMMvariational inequality |
| spellingShingle | Aifen Feng Xiaogai Chang Youlin Shang Jingya Fan Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model Mathematics partially linear model B-spline interpolation ADMM variational inequality |
| title | Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model |
| title_full | Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model |
| title_fullStr | Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model |
| title_full_unstemmed | Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model |
| title_short | Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model |
| title_sort | application of the admm algorithm for a high dimensional partially linear model |
| topic | partially linear model B-spline interpolation ADMM variational inequality |
| url | https://www.mdpi.com/2227-7390/10/24/4767 |
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