Robust model-based clustering and mixture modeling by using trimming Luis A. Garc´ ıa-Escudero, Alfonso Gordaliza, Carlos Matr´ an and Agust´ ın Mayo-Iscar Abstract The use of trimming procedures is common in several statistical frame- works to achieve robustness against anomalous observations. Trimming can be also applied in model-based clustering and mixture modeling and this work reviews some trimming proposals aimed at robustifying these two widely used techniques. The consideration of computationally feasible constraints on the scatters of the clus- ters and mixture components also plays an important role in these proposals. This work also presents some recent extensions of these methods to related problems. Some new tools helping the user to fix the different tuning parameters are shown. Key words: Model-based clustering; mixture models; robustness; trimming 1 Introduction Trimming is surely the easiest and one of the most widely applied strategies to achieve robustness in statistical procedures and it simply means that certain fraction α of observations are not taking into account when applying the statistical proce- Luis Angel Garc´ ıa-Escudero Departamento de Estad´ ıstica e I.O. and IMUVA, Facultad de Ciencias. Universidad de Valladolid. 47002, Valladolid. Spain, e-mail: lagarcia@eio.uva.es Alfonso Gordaliza Departamento de Estad´ ıstica e I.O. and IMUVA, Facultad de Ciencias. Universidad de Valladolid. 47002, Valladolid. Spain, e-mail: alfonsog@eio.uva.es Carlos Matr´ an Departamento de Estad´ ıstica e I.O. and IMUVA, Facultad de Ciencias. Universidad de Valladolid. 47002, Valladolid. Spain, e-mail: matran@eio.uva.es Agust´ ın Mayo-Iscar Departamento de Estad´ ıstica e I.O. and IMUVA, Facultad de Ciencias. Universidad de Valladolid. 47002, Valladolid. Spain, e-mail: agustinm@eio.uva.es 1