September 2023 Simultaneous outlier detection and variable selection for spatial Durbin model
Yi Cheng, Yunquan Song
Author Affiliations +
Braz. J. Probab. Stat. 37(3): 596-618 (September 2023). DOI: 10.1214/23-BJPS583


With the continuous development of economy and technology, the application of spatial data has become increasingly widespread. Handling complex spatial data, outlier detection has become an important problem in the study of spatial models. This article proposes a method for simultaneously performing outlier detection and variable selection in the spatial Durbin model. This method combines relevant theories of spatial statistics and enables accurate identification and location of outliers, as well as variable selection of estimation coefficients, by modeling and analyzing spatial data. The experimental results indicate that the proposed method effectively detects outliers in spatial data while maintaining accuracy, and has high interpretability and generalization value. Furthermore, a practical case is presented to demonstrate the method’s effectiveness in real-world scenarios.

Funding Statement

The researches are supported by the Fundamental Research Funds for the Central Universities (No.23CX03012A), National Key Research and Development Program of China (2021YFA1000102).


The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper. The corresponding author: Yunquan Song, E-mail address:


Download Citation

Yi Cheng. Yunquan Song. "Simultaneous outlier detection and variable selection for spatial Durbin model." Braz. J. Probab. Stat. 37 (3) 596 - 618, September 2023.


Received: 1 May 2023; Accepted: 1 August 2023; Published: September 2023
First available in Project Euclid: 22 November 2023

Digital Object Identifier: 10.1214/23-BJPS583

Keywords: outlier detection , Spatial Durbin model , Variable selection

Rights: Copyright © 2023 Brazilian Statistical Association


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Vol.37 • No. 3 • September 2023
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