Significance

We will provide a robust inference method that can be used in practice under reasonable assumptions. The implementation of our method will be feasible in terms of computing time. It will provide conservative confidence intervals with reasonable coverage levels, and at the same time will be efficient when no contamination is present in the data. We expect our method to be widely used in practice. We will provide a new way of performing robust inference in linear regression models. The theoretical results justifying our approach will be valid under mild assumptions. Unlike the classical bootstrap, our technique will be feasible in practical applications. We will develop a reliable, justified and usable tool to investigate the effect of atypical data points on linear regression analyses.