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Variable Selection for the Spatial Autoregressive Model with Autoregressive Disturbances

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  • Xuan Liu

    (School of Mathematics and Information Science, Nanchang Normal University, Nanchang 330032, China)

  • Jianbao Chen

    (College of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, China)

Abstract

Along with the rapid development of the geographic information system, high-dimensional spatial heterogeneous data has emerged bringing theoretical and computational challenges to statistical modeling and analysis. As a result, effective dimensionality reduction and spatial effect recognition has become very important. This paper focuses on variable selection in the spatial autoregressive model with autoregressive disturbances (SARAR) which contains a more comprehensive spatial effect. The variable selection procedure is presented by using the so-called penalized quasi-likelihood approach. Under suitable regular conditions, we obtain the rate of convergence and the asymptotic normality of the estimators. The theoretical results ensure that the proposed method can effectively identify spatial effects of dependent variables, find spatial heterogeneity in error terms, reduce the dimension, and estimate unknown parameters simultaneously. Based on step-by-step transformation, a feasible iterative algorithm is developed to realize spatial effect identification, variable selection, and parameter estimation. In the setting of finite samples, Monte Carlo studies and real data analysis demonstrate that the proposed penalized method performs well and is consistent with the theoretical results.

Suggested Citation

  • Xuan Liu & Jianbao Chen, 2021. "Variable Selection for the Spatial Autoregressive Model with Autoregressive Disturbances," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1448-:d:578793
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    1. Mu Yue & Jingxin Xi, 2025. "Sparse Boosting for Additive Spatial Autoregressive Model with High Dimensionality," Mathematics, MDPI, vol. 13(5), pages 1-16, February.

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