Efficient Estimation and Response Variable Selection in Sparse Partial Envelope Model
In this paper, we propose a sparse partial envelope model that performs response variable selection efficiently under the partial envelope model. We discuss its theoretical properties including consistency, an oracle property and the asymptotic distribution of the sparse partial envelope estimator....
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2024-11-01
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| Series: | Mathematics |
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| author | Yu Wu Jing Zhang |
| author_facet | Yu Wu Jing Zhang |
| author_sort | Yu Wu |
| collection | DOAJ |
| description | In this paper, we propose a sparse partial envelope model that performs response variable selection efficiently under the partial envelope model. We discuss its theoretical properties including consistency, an oracle property and the asymptotic distribution of the sparse partial envelope estimator. A large-sample situation and high-dimensional situation are both considered. Numerical experiments demonstrate that the sparse partial envelope estimator has excellent response variable selection performance both in the large-sample situation and the high-dimensional situation. Moreover, simulation studies and real data analysis suggest that the sparse partial envelope estimator has a much more competitive performance than the standard estimator, the oracle partial envelope estimator, the active partial envelope estimator and the sparse envelope estimator, whether it is in the large-sample situation or the high-dimensional situation. |
| format | Article |
| id | doaj-art-cd7c37b6b7e44b809004deecf75afbd1 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-cd7c37b6b7e44b809004deecf75afbd12024-12-13T16:27:39ZengMDPI AGMathematics2227-73902024-11-011223375810.3390/math12233758Efficient Estimation and Response Variable Selection in Sparse Partial Envelope ModelYu Wu0Jing Zhang1Business School, Nanjing University, Nanjing 210093, ChinaCollege of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, ChinaIn this paper, we propose a sparse partial envelope model that performs response variable selection efficiently under the partial envelope model. We discuss its theoretical properties including consistency, an oracle property and the asymptotic distribution of the sparse partial envelope estimator. A large-sample situation and high-dimensional situation are both considered. Numerical experiments demonstrate that the sparse partial envelope estimator has excellent response variable selection performance both in the large-sample situation and the high-dimensional situation. Moreover, simulation studies and real data analysis suggest that the sparse partial envelope estimator has a much more competitive performance than the standard estimator, the oracle partial envelope estimator, the active partial envelope estimator and the sparse envelope estimator, whether it is in the large-sample situation or the high-dimensional situation.https://www.mdpi.com/2227-7390/12/23/3758response variable selectiondimension reductionpartial envelope modelGrassmann manifoldoracle property |
| spellingShingle | Yu Wu Jing Zhang Efficient Estimation and Response Variable Selection in Sparse Partial Envelope Model Mathematics response variable selection dimension reduction partial envelope model Grassmann manifold oracle property |
| title | Efficient Estimation and Response Variable Selection in Sparse Partial Envelope Model |
| title_full | Efficient Estimation and Response Variable Selection in Sparse Partial Envelope Model |
| title_fullStr | Efficient Estimation and Response Variable Selection in Sparse Partial Envelope Model |
| title_full_unstemmed | Efficient Estimation and Response Variable Selection in Sparse Partial Envelope Model |
| title_short | Efficient Estimation and Response Variable Selection in Sparse Partial Envelope Model |
| title_sort | efficient estimation and response variable selection in sparse partial envelope model |
| topic | response variable selection dimension reduction partial envelope model Grassmann manifold oracle property |
| url | https://www.mdpi.com/2227-7390/12/23/3758 |
| work_keys_str_mv | AT yuwu efficientestimationandresponsevariableselectioninsparsepartialenvelopemodel AT jingzhang efficientestimationandresponsevariableselectioninsparsepartialenvelopemodel |