pp 1–19 | Cite as

Robust model-based clustering with mild and gross outliers

  • Alessio FarcomeniEmail author
  • Antonio Punzo
Original Paper


We propose a model-based clustering procedure where each component can take into account cluster-specific mild outliers through a flexible distributional assumption, and a proportion of observations is additionally trimmed. We propose a penalized likelihood approach for estimation and selection of the proportions of mild and gross outliers. A theoretically grounded penalty parameter is then obtained. Simulation studies illustrate the advantages of our procedure over flexible mixtures without trimming, and over trimmed normal mixture models (tclust). We conclude with an original real data example on the identification of the source from illicit drug shipments seized in Italy and Spain. The methodology proposed in this paper has been implemented in R functions which can be downloaded from


tclust Contaminated normal Penalized likelihood 

Mathematics Subject Classification

62H30 91C20 62F35 



The authors are grateful to two referees for constructive and helpful suggestions.

Supplementary material

11749_2019_693_MOESM1_ESM.pdf (83 kb)
Supplementary material 1 (pdf 83 KB)


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2019

Authors and Affiliations

  1. 1.Department of Economics and FinanceUniversity of Rome “Tor Vergata”RomeItaly
  2. 2.Department of Economics and BusinessUniversity of CataniaCataniaItaly

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