Optimal model selection in density estimation
Matthieu Lerasle (2012)
Annales de l'I.H.P. Probabilités et statistiques
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In order to calibrate a penalization procedure for model selection, the statistician has to choose a shape for the penalty and a leading constant. In this paper, we study, for the marginal density estimation problem, the resampling penalties as general estimators of the shape of an ideal penalty. We prove that the selected estimator satisfies sharp oracle inequalities without remainder terms under a few assumptions on the marginal density and the collection of models. We also study...