Abstract

Robust statistical analyses depend on tuning choices that balance protection against contamination and efficiency under the assumed model. We present monitoring as a practical framework for replacing a single robust fit with trajectories indexed by subset size or breakdown point. In regression, these trajectories reveal how residuals, coefficient evidence and outlier decisions change as atypical observations enter the fit, as illustrated by bank-customer data. Simulation results emphasize the difference between individual and simultaneous outlier testing, showing why default high-breakdown settings may overflag clean samples. Finally, fan plots connect transformation choice, particularly Box–Cox and Yeo–Johnson families, with outlier structure and reproducible model selection, and improve transparent reporting for applied statistical studies.