Estimation and Variable Selection for Quantile Regression of High-Dimensional Spatial Dependent Data with Endogenous Spatial Weight Matrix

Haiqiang Ma, Zhiyan Sheng, Xuan Liu, Jianbao Chen

Acta Mathematica Sinica, Chinese Series ›› 2025, Vol. 68 ›› Issue (2) : 240-267.

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Acta Mathematica Sinica, Chinese Series ›› 2025, Vol. 68 ›› Issue (2) : 240-267. DOI: 10.12386/A20230170

Estimation and Variable Selection for Quantile Regression of High-Dimensional Spatial Dependent Data with Endogenous Spatial Weight Matrix

  • Haiqiang Ma1, Zhiyan Sheng1, Xuan Liu2, Jianbao Chen3
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Abstract

With the development of big data technology, the dimensionality of spatial data is becoming higher and higher, and the endogeneity and heterogeneity of data often exist simultaneously. In this paper, we propose a quantile regression model of high-dimensional spatial dependent data with endogenous spatial weight matrix so as to analyze high-dimensional spatial dependent data robustly. We then develop a three-step penalized quantile estimation procedure through combining the instrumental variable method, variable selection method with robust statistic method, and establish the consistency and the asymptotic normality of the corresponding estimators. In addition, the oracle theoretical properties of variable selection are derived under some mild conditions. At last, we investigate the effectiveness and robustness of the proposed model and method through simulations and an application to housing prices in 284 prefecture-level cities across the country.

Key words

high-dimensional spatial dependence data / endogenous spatial weight matrix / heterogeneity / quantile regression / asymptotic property

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Haiqiang Ma , Zhiyan Sheng , Xuan Liu , Jianbao Chen. Estimation and Variable Selection for Quantile Regression of High-Dimensional Spatial Dependent Data with Endogenous Spatial Weight Matrix. Acta Mathematica Sinica, Chinese Series, 2025, 68(2): 240-267 https://doi.org/10.12386/A20230170

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