Adaptively Robust Geographically Weighted Regression

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.