Optimal model selection in density estimation

Autor(es)

Lerasle, Matthieu ^[1]

Afiliação do(s) autor(es)

^[1] IME USP, INSA Toulouse, Inst Math Toulouse, CNRS, UMR 5219, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES; v. 48, n. 3, p. 884-908, AUG 2012.
• Citações Web of Science: 10

Resumo

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 s and the collection of models. We also study the slope heuristic, which yields a data-driven choice of the leading constant in front of the penalty when the complexity of the models is well-chosen. (AU)

• Processo FAPESP: 09/09494-0 - Reamostragem e seleção de modelos para cadeias estocásticas com memória de alcance variável
• Beneficiário: Matthieu Pierre Lerasle
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado