We develop a new robust geographically weighted regression method in the presence of outliers. We embed the standard geographically weighted regression in robust objective function based on $\gamma$-divergence. A novel feature of the proposed approach is that two tuning parameters that control robustness and spatial smoothness are automatically tuned in a data-dependent manner. Further, the proposed method can produce robust standard error estimates and give us a reasonable quantity for local outlier detection. We demonstrate that the proposed method is superior to the existing robust geographically weighted regression through simulation and data analysis.

中文翻译：

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自适应稳健的地理加权回归

我们在存在异常值的情况下开发了一种新的稳健的地理加权回归方法。我们将标准的地理加权回归嵌入到稳健的目标函数中$\gamma$-分歧。所提出的方法的一个新特点是控制鲁棒性和空间平滑度的两个调整参数以数据相关的方式自动调整。此外，所提出的方法可以产生稳健的标准误差估计，并为我们提供合理的数量用于局部异常值检测。我们通过模拟和数据分析证明了所提出的方法优于现有的鲁棒地理加权回归。