Sufficient dimension reduction for regression with spatially correlated errors: application to prediction
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915138429255680 |
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| author | Forzani, Liliana Arancibia, Rodrigo García Gieco, Antonella Llop, Pamela Yao, Anne |
| author_facet | Forzani, Liliana Arancibia, Rodrigo García Gieco, Antonella Llop, Pamela Yao, Anne |
| contents | In this paper, we address the problem of predicting a response variable in the context of both, spatially correlated and high-dimensional data. To reduce the dimensionality of the predictor variables, we apply the sufficient dimension reduction (SDR) paradigm, which reduces the predictor space while retaining relevant information about the response. To achieve this, we impose two different spatial models on the inverse regression: the separable spatial covariance model (SSCM) and the spatial autoregressive error model (SEM). For these models, we derive maximum likelihood estimators for the reduction and use them to predict the response via nonparametric rules for forward regression. Through simulations and real data applications, we demonstrate the effectiveness of our approach for spatial data prediction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02781 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sufficient dimension reduction for regression with spatially correlated errors: application to prediction Forzani, Liliana Arancibia, Rodrigo García Gieco, Antonella Llop, Pamela Yao, Anne Methodology Statistics Theory In this paper, we address the problem of predicting a response variable in the context of both, spatially correlated and high-dimensional data. To reduce the dimensionality of the predictor variables, we apply the sufficient dimension reduction (SDR) paradigm, which reduces the predictor space while retaining relevant information about the response. To achieve this, we impose two different spatial models on the inverse regression: the separable spatial covariance model (SSCM) and the spatial autoregressive error model (SEM). For these models, we derive maximum likelihood estimators for the reduction and use them to predict the response via nonparametric rules for forward regression. Through simulations and real data applications, we demonstrate the effectiveness of our approach for spatial data prediction. |
| title | Sufficient dimension reduction for regression with spatially correlated errors: application to prediction |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2502.02781 |