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Statistical Methods & Applications

, Volume 27, Issue 4, pp 609–619 | Cite as

Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini

  • Claudio Agostinelli
  • Luca Greco
Original Paper

Abstract

Andrea Cerioli, Marco Riani, Anthony Atkinson, Aldo Corbellini (CRAC hereafter) have presented a powerful methodology aimed at improving robust fitting and related diagnostic tools. Monitoring is a very flexible approach that allows to tune the selected robust technique by looking at a whole movie of the available data. We contribute to the discussion of CRAC’s paper by applying the principle of monitoring to multivariate weighted likelihood estimation. The reliability of the method is illustrated through the analysis of the datasets taken from CRAC’ s paper.

Keywords

Monitoring Outliers Pearson residuals Robust distances Weighted likelihood 

References

  1. Agostinelli C (2002) Robust model selection in regression via weighted likelihood methodology. Stat Probab Lett 56:289–300MathSciNetCrossRefzbMATHGoogle Scholar
  2. Agostinelli C, Greco L (2013) A weighted strategy to handle likelihood uncertainty in Bayesian inference. Comput Stat 28(1):319–339MathSciNetCrossRefzbMATHGoogle Scholar
  3. Agostinelli C, Greco L (2017) Weighted likelihood estimation of multivariate location and scatter. arXiv preprint arXiv:1706.05876
  4. Agostinelli C, Markatou M (1998) A one-step robust estimator for regression based on the weighted likelihood reweighting scheme. Stat Probab Lett 37(4):341–350MathSciNetCrossRefzbMATHGoogle Scholar
  5. Alqallaf F, Agostinelli C (2016) Robust inference in generalized linear models. Commun Stat Simul Comput 45(9):3053–3073MathSciNetCrossRefzbMATHGoogle Scholar
  6. Basu A, Lindsay BG (1994) Minimum disparity estimation for continuous models: efficiency, distributions and robustness. Ann Inst Stat Math 46(4):683–705MathSciNetCrossRefzbMATHGoogle Scholar
  7. Farcomeni A, Greco L (2016) Robust methods for data reduction. CRC press, Boca Raton, FLzbMATHGoogle Scholar
  8. Greco L (2016) Weighted likelihood based inference for \(p(x < y)\). Commun Stat Simul Comput. https://doi.org/10.1080/03610918.2016.1252396
  9. Huber P (1985) Projection pursuit. Ann Stat 13(2):435–475MathSciNetCrossRefzbMATHGoogle Scholar
  10. Lindsay B (1994) Efficiency versus robustness: the case for minimum hellinger distance and related methods. Ann Stat 22:1018–1114MathSciNetCrossRefzbMATHGoogle Scholar
  11. Markatou M, Basu A, Lindsay BG (1998) Weighted likelihood equations with bootstrap root search. J Am Stat Assoc 93(442):740–750MathSciNetCrossRefzbMATHGoogle Scholar
  12. Park C, Basu A, Lindsay B (2002) The residual adjustment function and weighted likelihood: a graphical interpretation of robustness of minimum disparity estimators. Comput Stat Data Anal 39(1):21–33MathSciNetCrossRefzbMATHGoogle Scholar
  13. Scott D, Wand M (1991) Feasibility of multivariate density estimates. Biometrika 78(1):197–205MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TrentoTrentoItaly
  2. 2.DEMM DepartmentUniversity of SannioBeneventoItaly

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