Choice of estimators based on Kullback-Leibler risk

Estimators choice is a crucial topic in statistics. The most famous criterion is the Akaike information criterion. It has been constructed as an approximation, up to a constant, of the Kullback-Leibler risk. However, a precise value of the Akaike criterion has no direct interpretation and its variability is often ignored. We propose several approaches to estimate Kullback-Leibler risks. The criteria defined can be used in a parametric, non-parametric or semi-parametric context. An extension of these criteria for incomplete data is presented. The issue of the choice of estimators in the presence of incomplete data is described. Several applications in the survival framework is described: smooth estimators choice for the hazard function, estimators choice from proportional hazard model and stratified model, and estimators choice for markov model and non markov model. Finally, several criteria are defined for selecting estimators based on different observations.