Statistical Methods & Applications

, Volume 27, Issue 4, pp 661–666 | Cite as

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

  • Andrea CerioliEmail author
  • Marco Riani
  • Anthony C. Atkinson
  • Aldo Corbellini
Original Paper

We thank the Editor, Tommaso Proietti, for the invitation to write a discussion paper and for encouraging such a wide ranging discussion. We also thank the Associate Editor in charge of the discussion, Alessio Farcomeni, for his very careful work.

We feel humbled by the quantity of insightful comments stimulated by our paper and that so many prominent researchers in the field of robust statistics were kind enough to contribute to the discussion. We are also highly surprised (and very glad) to see that the length of the discussion is twice the length of the original paper!

We thank all the discussants for their supportive comments and for their appreciation of our work. Therefore, we take the discussion as a good sign that the “philosophy” of monitoring will have more fans in the future. We believe that the discussions include contributions that are worth considering per se: improvements of existing methodologies; extensions to multi-parameter monitoring; a new \(\rho \)



The work has been partially supported by the European Commission’s Hercule III programme 2014–2020 through the Automated Monitoring Tool project. This research benefits from the HPC (High Performance Computing) facility of the University of Parma, Italy. M.R. gratefully acknowledges support from the CRoNoS project, reference CRoNoS COST Action IC1408.


  1. Agostinelli C, Greco L (2018) Weighted likelihood estimation of multivariate location and scatter. Test. Google Scholar
  2. Andrews DF, Bickel PJ, Hampel FR, Tukey WJ, Huber PJ (1972) Robust estimates of location: survey and advances. Princeton University Press, PrincetonzbMATHGoogle Scholar
  3. Atkinson AC (1973) Testing transformations to normality. J R Stat Soc Ser B 35:473–479MathSciNetzbMATHGoogle Scholar
  4. Box GEP (1953) Non-normality and tests on variances. Biometrika 40:318–335MathSciNetCrossRefzbMATHGoogle Scholar
  5. Box GEP, Cox DR (1964) An analysis of transformations (with discussion). J R Stat Soc Ser B 26:211–246MathSciNetzbMATHGoogle Scholar
  6. Cerioli A, Riani M (2003) Robust methods for the analysis of spatially autocorrelated data. Stat Methods Appl 11:335–358CrossRefzbMATHGoogle Scholar
  7. Cerioli A, Atkinson AC, Riani M (2016) How to marry robustness and applied statistics. In: Di Battista T, Moreno E, Racugno W (eds) Topics on methodological and applied statistical inference. Springer, Heidelberg, pp 51–64Google Scholar
  8. Cerioli A, Farcomeni A, Riani M (2018) Wild adaptive trimming for robust estimation and cluster analysis. Scand J Stat. Google Scholar
  9. Dotto F, Farcomeni A, García-Escudero LA, Mayo-Iscar A (2018) A reweighting approach to robust clustering. Stat Comput 28:477–493MathSciNetCrossRefzbMATHGoogle Scholar
  10. Filzmoser P, Ruiz-Gazen A, Thomas-Agnan C (2014) Identification of local multivariate outliers. Stat Pap 55:29–47MathSciNetCrossRefzbMATHGoogle Scholar
  11. Riani M, Atkinson AC (2000) Robust diagnostic data analysis: transformations in regression (with discussion). Technometrics 42:384–398MathSciNetCrossRefzbMATHGoogle Scholar
  12. Riani M, Atkinson AC (2010) Robust model selection with flexible trimming. Comput Stat Data Anal 54:3300–3312MathSciNetCrossRefzbMATHGoogle Scholar
  13. Riani M, Cerioli A, Atkinson AC, Perrotta D (2014) Monitoring robust regression. Electron J Stat 8:646–677MathSciNetCrossRefzbMATHGoogle Scholar
  14. Riani M, Atkinson AC, Cerioli A, Corbellini A (2018) Robust methods via monitoring for clustering and multivariate data analysis. SubmittedGoogle Scholar
  15. Rousseeuw PJ, Van Den Bossche W (2018) Detecting deviating data cells. Technometrics 60:135–145MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Economics and ManagementUniversity of ParmaParmaItaly
  2. 2.Department of StatisticsThe London School of EconomicsLondonUK

Personalised recommendations