In nonparametric statistics a classical optimality criterion for estimation procedures isprovided by the minimax rate of convergence. However this point of view can be subject tocontroversy as it requires to look for the worst behavior of an estimation procedure in agiven space. The purpose of this paper is to introduce a new criterion based on genericbehavior of estimators. We are here interested in the rate of convergence obtained withsome classical estimators on almost every, in the sense of prevalence, function in a Besovspace. We also show that generic results coincide with minimax ones in these cases.
