Functional Partial Least-Squares: Adaptive Estimation and Inference
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915275893374976 |
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| author | Babii, Andrii Carrasco, Marine Tsafack, Idriss |
| author_facet | Babii, Andrii Carrasco, Marine Tsafack, Idriss |
| contents | We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains nearly minimax-optimal convergence rates over a class of ellipsoids and propose an adaptive early stopping procedure for selecting the number of PLS components. In addition, we develop new test that can detect local alternatives converging at the parametric rate which can be inverted to construct confidence sets. Simulation results demonstrate that the estimator performs favorably relative to several existing methods and the proposed test exhibits good power properties. We apply our methodology to evaluate the nonlinear effects of temperature on corn and soybean yields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11134 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Functional Partial Least-Squares: Adaptive Estimation and Inference Babii, Andrii Carrasco, Marine Tsafack, Idriss Statistics Theory Econometrics Computation Methodology Machine Learning 62G05, 62G08 We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains nearly minimax-optimal convergence rates over a class of ellipsoids and propose an adaptive early stopping procedure for selecting the number of PLS components. In addition, we develop new test that can detect local alternatives converging at the parametric rate which can be inverted to construct confidence sets. Simulation results demonstrate that the estimator performs favorably relative to several existing methods and the proposed test exhibits good power properties. We apply our methodology to evaluate the nonlinear effects of temperature on corn and soybean yields. |
| title | Functional Partial Least-Squares: Adaptive Estimation and Inference |
| topic | Statistics Theory Econometrics Computation Methodology Machine Learning 62G05, 62G08 |
| url | https://arxiv.org/abs/2402.11134 |