Robust Variable Selection with Exponential Squared Loss for the Spatial Error Model
With the widespread application of spatial data in fields like econometrics and geographic information science, the methods to enhance the robustness of spatial econometric model estimation and variable selection have become a central focus of research. In the context of the spatial error model (SEM...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/13/1/4 |
| _version_ | 1797344592546234368 |
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| author | Shida Ma Yiming Hou Yunquan Song Feng Zhou |
| author_facet | Shida Ma Yiming Hou Yunquan Song Feng Zhou |
| author_sort | Shida Ma |
| collection | DOAJ |
| description | With the widespread application of spatial data in fields like econometrics and geographic information science, the methods to enhance the robustness of spatial econometric model estimation and variable selection have become a central focus of research. In the context of the spatial error model (SEM), this paper introduces a variable selection method based on exponential square loss and the adaptive lasso penalty. Due to the non-convex and non-differentiable nature of this proposed method, convex programming is not applicable for its solution. We develop a block coordinate descent algorithm, decompose the exponential square component into the difference of two convex functions, and utilize the CCCP algorithm in combination with parabolic interpolation for optimizing problem-solving. Numerical simulations demonstrate that neglecting the spatial effects of error terms can lead to reduced accuracy in selecting zero coefficients in SEM. The proposed method demonstrates robustness even when noise is present in the observed values and when the spatial weights matrix is inaccurate. Finally, we apply the model to the Boston housing dataset. |
| first_indexed | 2024-03-08T11:05:56Z |
| format | Article |
| id | doaj.art-0956ea67dc274e61a16e54014578b2d0 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-08T11:05:56Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-0956ea67dc274e61a16e54014578b2d02024-01-26T15:02:43ZengMDPI AGAxioms2075-16802023-12-01131410.3390/axioms13010004Robust Variable Selection with Exponential Squared Loss for the Spatial Error ModelShida Ma0Yiming Hou1Yunquan Song2Feng Zhou3College of Science, China University of Petroleum, Qingdao 266580, ChinaCollege of Science, China University of Petroleum, Qingdao 266580, ChinaCollege of Science, China University of Petroleum, Qingdao 266580, ChinaCollege of Science, China University of Petroleum, Qingdao 266580, ChinaWith the widespread application of spatial data in fields like econometrics and geographic information science, the methods to enhance the robustness of spatial econometric model estimation and variable selection have become a central focus of research. In the context of the spatial error model (SEM), this paper introduces a variable selection method based on exponential square loss and the adaptive lasso penalty. Due to the non-convex and non-differentiable nature of this proposed method, convex programming is not applicable for its solution. We develop a block coordinate descent algorithm, decompose the exponential square component into the difference of two convex functions, and utilize the CCCP algorithm in combination with parabolic interpolation for optimizing problem-solving. Numerical simulations demonstrate that neglecting the spatial effects of error terms can lead to reduced accuracy in selecting zero coefficients in SEM. The proposed method demonstrates robustness even when noise is present in the observed values and when the spatial weights matrix is inaccurate. Finally, we apply the model to the Boston housing dataset.https://www.mdpi.com/2075-1680/13/1/4spatial error modelexponential square lossadaptive lassorobust variable selection |
| spellingShingle | Shida Ma Yiming Hou Yunquan Song Feng Zhou Robust Variable Selection with Exponential Squared Loss for the Spatial Error Model Axioms spatial error model exponential square loss adaptive lasso robust variable selection |
| title | Robust Variable Selection with Exponential Squared Loss for the Spatial Error Model |
| title_full | Robust Variable Selection with Exponential Squared Loss for the Spatial Error Model |
| title_fullStr | Robust Variable Selection with Exponential Squared Loss for the Spatial Error Model |
| title_full_unstemmed | Robust Variable Selection with Exponential Squared Loss for the Spatial Error Model |
| title_short | Robust Variable Selection with Exponential Squared Loss for the Spatial Error Model |
| title_sort | robust variable selection with exponential squared loss for the spatial error model |
| topic | spatial error model exponential square loss adaptive lasso robust variable selection |
| url | https://www.mdpi.com/2075-1680/13/1/4 |
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