Adaptively Robust Geographically Weighted Regression

TL;DR

This paper introduces a new robust geographically weighted regression method that automatically tunes robustness and spatial smoothness parameters, effectively handling outliers and enabling local outlier detection.

Contribution

It presents a novel robust GWR approach using $ ext{gamma}$-divergence with data-driven tuning of parameters, improving outlier resistance and interpretability.

Findings

Outperforms existing robust GWR methods in simulations

Provides reliable standard error estimates for robust parameters

Enables effective local outlier detection

Abstract

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.