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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2311.12597 |
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| _version_ | 1866910711137959936 |
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| author | Yang, Dan Shao, Jianlong Shen, Haipeng Zhu, Hongtu |
| author_facet | Yang, Dan Shao, Jianlong Shen, Haipeng Zhu, Hongtu |
| contents | Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices when observed at grid points. To avoid the inefficiency of the classical method involving estimation of a two-dimensional coefficient function, we propose a functional bilinear regression model, and introduce an innovative three-term penalty to impose roughness penalty in the estimation. The proposed estimator exhibits minimax optimal property for prediction under the framework of reproducing kernel Hilbert space. An iterative generalized cross-validation approach is developed to choose tuning parameters, which significantly improves the computational efficiency over the traditional cross-validation approach. The statistical and computational advantages of the proposed method over existing methods are further demonstrated via simulated experiments, the Canadian weather data, and a biochemical long-range infrared light detection and ranging data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_12597 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal Functional Bilinear Regression with Two-way Functional Covariates via Reproducing Kernel Hilbert Space Yang, Dan Shao, Jianlong Shen, Haipeng Zhu, Hongtu Methodology Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices when observed at grid points. To avoid the inefficiency of the classical method involving estimation of a two-dimensional coefficient function, we propose a functional bilinear regression model, and introduce an innovative three-term penalty to impose roughness penalty in the estimation. The proposed estimator exhibits minimax optimal property for prediction under the framework of reproducing kernel Hilbert space. An iterative generalized cross-validation approach is developed to choose tuning parameters, which significantly improves the computational efficiency over the traditional cross-validation approach. The statistical and computational advantages of the proposed method over existing methods are further demonstrated via simulated experiments, the Canadian weather data, and a biochemical long-range infrared light detection and ranging data. |
| title | Optimal Functional Bilinear Regression with Two-way Functional Covariates via Reproducing Kernel Hilbert Space |
| topic | Methodology |
| url | https://arxiv.org/abs/2311.12597 |