Why minimax is not that pessimistic

Abstract

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