Model selection in density estimation via cross-validation

摘要: The problem of model selection by cross-validation is addressed in the density estimation framework. Extensively used practice, (CV) remains poorly understood, especially non-asymptotic setting which main concern this work. A recurrent with CV computation time it involves. This drawback overcome here thanks to closed-form expressions for estimator risk a broad class widespread estimators: projection estimators. In order shed new lights on procedures respect cardinality $p$ test set, interpreted as penalized criterion random penalty. For instance, amount penalization shown increase $p$. theoretical assessment performance carried out two oracle inequalities applying respectively bounded or square-integrable densities. several collections models, adaptivity results Holder and Besov spaces are derived well.