Assessing when a sample is mostly normal

The use of trimming procedures constitutes a natural approach to robustifying statistical 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 L2-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, introducing 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.