Statistical applications of over-fitting due to trimmings

Pedro Alvarez-Esteban

Universidad de Valladolid, Spain

Roughly speaking, the underlying principle that we will explore, says that if two random samples of the same probability distribution are partially trimmed to make them as similar as possible, then you should be able to distinguish these pair of trimmed samples from any other pair of non-trimmed samples of the same sizes. In this talk, our goal will be to provide sound and empirical evidence of this affirmation and design a general bootstrap procedure for comparison of two samples or one sample and a given distribution. This statistical procedure should be also useful in other frameworks of model validation. As an added value of the principle, we provide an appealing methodology to analyze, from a non-parametrical point of view, if we can assume that k samples arise from essentially identical underlying structures.