Assessing when a sample is mostly normal Pedro C. Alvarez-Esteban a,* Eustasio del Barrio a Juan A. Cuesta-Albertos b CarlosMatr´an a a Dept. de Estad´ ıstica e Investigaci´on Operativa, Universidad de Valladolid. Prado de la Magdalena s.n., 47005 Valladolid. Spain. b Dept.Matem´aticas,Estad´ ıstica y Computaci´on, Universidad de Cantabria. Avda. los Castros s.n. 39005 Santander, Spain. Abstract The use of trimming procedures constitutes a natural approach to robustifying sta- tistical methods. This is the case of goodness-of-fit tests based on a distance, which can be modified by choosing trimmed versions of the distributions minimizing that distance. In this paper we consider the L 2 -Wasserstein distance and introduce the trimming methodology for assessing when a data sample can be considered mostly normal. The method can be extended to other location and scale models, intro- ducing a robust approach to model validation, and allows an additional descriptive analysis by determining the subset of the data with the best improved fit to the model. This is a consequence of our use of data-driven trimming methods instead of more classical symmetric trimming procedures. Key words: Model Assessment, Asymptotics, Impartial Trimming, Wasserstein distance, Similarity. 1 Introduction. Trimming methods are a main tool in the design of robust statistical proce- dures. For univariate data a classical way of trimming is based on deleting the same proportion of observations in each tail of the distribution. This approach * Email address: pedroc@eio.uva.es (Pedro C. Alvarez-Esteban). 1 Research partially supported by the Spanish Ministerio de Educaci´on y Cien- cia, grant MTM2008-06067-C02-01, and 02 and by the Consejer´ ıa de Educaci´on y Cultura de la Junta de Castilla y Le´on, GR150. Preprint submitted to Elsevier 29 January 2009