Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample”

In this comment on the discussion paper The power of monitoring: how to make the most of a contaminated multivariate sample by A. Cerioli, M. Riani, A. Atkinson and A. Corbellini, we describe how the hard rejection property of the MCD method can be mimicked by an S-estimator with appropriate rho-function. We also point the reader to fast and deterministic algorithms for the MCD, S- and MM-estimators that are specifically suited for monitoring experiments. They were made available a few years ago and successfully used for monitoring in our papers. Finally, the question is raised how monitoring can be applied or extended for increasing numbers of cases, variables and tuning parameters.