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

@article{Raymaekers2018DiscussionO,
  title={Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample”},
  author={Jakob Raymaekers and Peter J. Rousseeuw and Iwein Vranckx},
  journal={Statistical Methods \& Applications},
  year={2018},
  volume={27},
  pages={589-594}
}
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… 
Penalised robust estimators for sparse and high-dimensional linear models
TLDR
A new class of robust M -estimators for performing simultaneous parameter estimation and variable selection in high-dimensional regression models and a fast accelerated proximal gradient algorithm, of coordinate descent type, is proposed and implemented for computing the estimates.

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