A Robust Estimation Approach for Mean-Shift and Variance-Inflation Outliers

We consider a classical regression model contaminated by multiple outliers arising simultaneously from mean-shift and variance-inflation mechanisms—which are generally considered as alternative. Identifying multiple outliers leads to computational challenges in the usual variance-inflation framework. We propose the use of robust estimation techniques to identify outliers arising from each mechanism, and we rely on restricted maximum likelihood estimation to accommodate variance-inflated outliers into the model. Furthermore, we introduce diagnostic plots which help to guide the analysis. We compare classical and robust methods with our novel approach on both simulated and real data.