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<p>Spatially varying-coefficient models (SVCMs) are a classical statistical tool designed to address non-stationary relationships between variables across geographic space. Existing estimation methods for SVCMs are all based on ordinary least squares (OLS), which are not robust to outliers in response measurements or heavy-tailed error distributions. To address this issue, in this paper we propose a robust estimation approach for SVCMs using bivariate spline approximation technique. We establish the consistency and asymptotic normality of the proposed estimator. The proposed method is further illustrated by simulation studies which demonstrate the finite sample performance of the method, and is applied in an empirical analysis.</p>

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Robust estimation for spatially varying-coefficient models

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Wenjuan Ma,
  • Xuejun Wang,
  • Riquan Zhang,
  • Hanbing Zhu

摘要

Spatially varying-coefficient models (SVCMs) are a classical statistical tool designed to address non-stationary relationships between variables across geographic space. Existing estimation methods for SVCMs are all based on ordinary least squares (OLS), which are not robust to outliers in response measurements or heavy-tailed error distributions. To address this issue, in this paper we propose a robust estimation approach for SVCMs using bivariate spline approximation technique. We establish the consistency and asymptotic normality of the proposed estimator. The proposed method is further illustrated by simulation studies which demonstrate the finite sample performance of the method, and is applied in an empirical analysis.