  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.
