Quantile regression for additive coefficient models in high dimensions
In this paper, we consider quantile regression in additive coefficient models (ACM) with high dimensionality under a sparsity assumption and approximate the additive coefficient functions by B-spline expansion. First, we consider the oracle estimator for quantile ACM when the number of additive coef...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2020
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| Online Access: | https://hdl.handle.net/10356/140938 |
| _version_ | 1826127944416755712 |
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| author | Fan, Zengyan Lian, Heng |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Fan, Zengyan Lian, Heng |
| author_sort | Fan, Zengyan |
| collection | NTU |
| description | In this paper, we consider quantile regression in additive coefficient models (ACM) with high dimensionality under a sparsity assumption and approximate the additive coefficient functions by B-spline expansion. First, we consider the oracle estimator for quantile ACM when the number of additive coefficient functions is diverging. Then we adopt the SCAD penalty and investigate the non-convex penalized estimator for model estimation and variable selection. Under some regularity conditions, we prove that the oracle estimator is a local solution of the SCAD penalized quantile regression problem. Simulation studies and an application to a genome-wide association study show that the proposed method yields good numerical results. |
| first_indexed | 2024-10-01T07:16:48Z |
| format | Journal Article |
| id | ntu-10356/140938 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:16:48Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1409382020-06-03T02:59:31Z Quantile regression for additive coefficient models in high dimensions Fan, Zengyan Lian, Heng School of Physical and Mathematical Sciences Science::Mathematics Additive Coefficient Models B-splines In this paper, we consider quantile regression in additive coefficient models (ACM) with high dimensionality under a sparsity assumption and approximate the additive coefficient functions by B-spline expansion. First, we consider the oracle estimator for quantile ACM when the number of additive coefficient functions is diverging. Then we adopt the SCAD penalty and investigate the non-convex penalized estimator for model estimation and variable selection. Under some regularity conditions, we prove that the oracle estimator is a local solution of the SCAD penalized quantile regression problem. Simulation studies and an application to a genome-wide association study show that the proposed method yields good numerical results. 2020-06-03T02:59:31Z 2020-06-03T02:59:31Z 2017 Journal Article Fan, Z., & Lian, H. (2018). Quantile regression for additive coefficient models in high dimensions. Journal of Multivariate Analysis, 164, 54-64. doi:10.1016/j.jmva.2017.11.001 0047-259X https://hdl.handle.net/10356/140938 10.1016/j.jmva.2017.11.001 2-s2.0-85035361839 164 54 64 en Journal of Multivariate Analysis © 2017 Elsevier Inc. All rights reserved. |
| spellingShingle | Science::Mathematics Additive Coefficient Models B-splines Fan, Zengyan Lian, Heng Quantile regression for additive coefficient models in high dimensions |
| title | Quantile regression for additive coefficient models in high dimensions |
| title_full | Quantile regression for additive coefficient models in high dimensions |
| title_fullStr | Quantile regression for additive coefficient models in high dimensions |
| title_full_unstemmed | Quantile regression for additive coefficient models in high dimensions |
| title_short | Quantile regression for additive coefficient models in high dimensions |
| title_sort | quantile regression for additive coefficient models in high dimensions |
| topic | Science::Mathematics Additive Coefficient Models B-splines |
| url | https://hdl.handle.net/10356/140938 |
| work_keys_str_mv | AT fanzengyan quantileregressionforadditivecoefficientmodelsinhighdimensions AT lianheng quantileregressionforadditivecoefficientmodelsinhighdimensions |