Trimming, optimal transportation, overfitting and statistical applications

Abstract : We present some ideas about \textitessential model validation based on trimming and the minimal distance method. We argue about the interest of the Wasserstein metric in this sense and show the connection in this case of essential model checking to a problem of optimal incomplete transportation of mass. We describe also some unexpected overfitting effect caused by trimming and provide pointers to relevant literature in which this overfitting is used for some statistical applications.