Spatial function-on-function regression
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916538961887232 |
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| author | Beyaztas, Ufuk Shang, Han Lin Sezer, Gizel Bakicierler Mandal, Abhijit Zoh, Roger S. Tekwe, Carmen D. |
| author_facet | Beyaztas, Ufuk Shang, Han Lin Sezer, Gizel Bakicierler Mandal, Abhijit Zoh, Roger S. Tekwe, Carmen D. |
| contents | We introduce a spatial function-on-function regression model to capture spatial dependencies in functional data by integrating spatial autoregressive techniques with functional principal component analysis. The proposed model addresses a critical gap in functional regression by enabling the analysis of functional responses influenced by spatially correlated functional predictors, a common scenario in fields such as environmental sciences, epidemiology, and socio-economic studies. The model employs a spatial functional principal component decomposition on the response and a classical functional principal component decomposition on the predictor, transforming the functional data into a finite-dimensional multivariate spatial autoregressive framework. This transformation allows efficient estimation and robust handling of spatial dependencies through least squares methods. In a series of extensive simulations, the proposed model consistently demonstrated superior performance in estimating both spatial autocorrelation and regression coefficient functions compared to some favorably existing traditional approaches, particularly under moderate to strong spatial effects. Application of the proposed model to Brazilian COVID-19 data further underscored its practical utility, revealing critical spatial patterns in confirmed cases and death rates that align with known geographic and social interactions. An R package provides a comprehensive implementation of the proposed estimation method, offering a user-friendly and efficient tool for researchers and practitioners to apply the methodology in real-world scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17327 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spatial function-on-function regression Beyaztas, Ufuk Shang, Han Lin Sezer, Gizel Bakicierler Mandal, Abhijit Zoh, Roger S. Tekwe, Carmen D. Methodology Computation 62R10 We introduce a spatial function-on-function regression model to capture spatial dependencies in functional data by integrating spatial autoregressive techniques with functional principal component analysis. The proposed model addresses a critical gap in functional regression by enabling the analysis of functional responses influenced by spatially correlated functional predictors, a common scenario in fields such as environmental sciences, epidemiology, and socio-economic studies. The model employs a spatial functional principal component decomposition on the response and a classical functional principal component decomposition on the predictor, transforming the functional data into a finite-dimensional multivariate spatial autoregressive framework. This transformation allows efficient estimation and robust handling of spatial dependencies through least squares methods. In a series of extensive simulations, the proposed model consistently demonstrated superior performance in estimating both spatial autocorrelation and regression coefficient functions compared to some favorably existing traditional approaches, particularly under moderate to strong spatial effects. Application of the proposed model to Brazilian COVID-19 data further underscored its practical utility, revealing critical spatial patterns in confirmed cases and death rates that align with known geographic and social interactions. An R package provides a comprehensive implementation of the proposed estimation method, offering a user-friendly and efficient tool for researchers and practitioners to apply the methodology in real-world scenarios. |
| title | Spatial function-on-function regression |
| topic | Methodology Computation 62R10 |
| url | https://arxiv.org/abs/2412.17327 |