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 of the robust estimator and give us a reasonable quantity for local outlier detection. We demonstrate that the proposed method is superior to the existing robust version of geographically weighted regression through simulation and data analysis.

翻译：我们开发了一种新的稳健的地理加权回归法,在外部线存在的情况下,我们将标准地理加权回归法嵌入基于$\gamma$-digence的稳健客观功能中。拟议方法的新特点之一是,两个控制稳健性和空间平滑性的调试参数会自动地以数据独立的方式调整。此外,拟议方法可以产生稳健的估算测算器的稳健的标准误差估计数,并给我们一个合理的数量供本地异差检测。我们证明,拟议方法优于通过模拟和数据分析的现有稳健版的地理加权回归法。