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

Abstract

We contribute to the discussion of an article where Andrea Cerioli, Marco Riani, Anthony Atkinson and Aldo Corbellini review the advantages of analyzing multivariate data by monitoring how the estimated model parameters change as the estimation parameters vary. The focus is on robust methods and their sensitivity to the nominal efficiency and breakdown point. In congratulating with the authors for the clear and stimulating exposition, we contribute to its discussion with an overview of what we experienced in applying the monitoring in our application domain.Keywords Forward Search · MM-estimation · S-estimation · Density estimation · Thinning · International trade data PrologueAndrea Cerioli, Marco Riani, Anthony Atkinson and Aldo Corbellini (hereafter CRAC) are passionate supporters of the data analysis approach proposed for this discussion (Cerioli et al. 2018), which consists in monitoring the model parameters estimated for a reasonable range of values of the key parameters of the estimation method, and selecting those producing the best results. Robust estimation algorithms depend on several tuning constants, producing effects that should be monitored. CRAC focus on the key parameters used to specify the maximum possible breakdown or efficiency to be achieved. We would like to complement their exposition with recent B Francesca Torti

Forum on Benford’s law and statistical methods for the detection of frauds

“…Nor would it be justifiable to change approach and model choices depending on the dataset under scrutiny: a coherent and sufficiently general approach is what this contribution tries to provide. With this effort, the authors bring ahead ideas that were discussed in recent years by an issue of this journal addressing the general theory of monitoring (Cerioli et al 2018) covering, among different methodological and practical issues, also a customs-fraud application (Perrotta and Torti 2018).…”

Assessing trimming methodologies for clustering linear regression data

“…The results seem rarely sensitive to the choice of the tuning constants, which in our FSDA implementation are chosen to cover the most typical scenarios. Frameworks for monitoring the effects of parameters and tuning constants have been discussed in clustering by Cerioli et al (2017) and some discussants (García-Escudero et al 2017b;Farcomeni and Dotto 2018;Perrotta and Torti 2018).…”