Estimator selection: a new method with applications to kernel density estimation
| Autor: | Claire Lacour, Pascal Massart, Vincent Rivoirard |
|---|---|
| Přispěvatelé: | Model selection in statistical learning (SELECT), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Mathematical optimization Computer science Kernel density estimation Selection strategy Mathematics - Statistics Theory Penalization Methods Statistics Theory (math.ST) 01 natural sciences 010104 statistics & probability [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] FOS: Mathematics Concentration Inequalities Minimal penalty Empirical risk minimization 0101 mathematics 010102 general mathematics Bandwidth (signal processing) Nonparametric statistics Estimator Density estimation Estimator Selection Oracle Inequality Pairwise comparison Statistics Probability and Uncertainty |
| Zdroj: | Sankhya A Sankhya A, Springer Verlag, 2017, 79 (2), pp.298-335. ⟨10.1007/s13171-017-0107-5⟩ Sankhya A, 2017, 79 (2), pp.298-335. ⟨10.1007/s13171-017-0107-5⟩ |
| ISSN: | 0972-7671 0976-836X |
| DOI: | 10.1007/s13171-017-0107-5⟩ |
| Popis: | International audience; Estimator selection has become a crucial issue in non parametric estimation. Two widely used methods are penalized empirical risk minimization (such as penalized log-likelihood estimation) or pairwise comparison (such as Lepski's method). Our aim in this paper is twofold. First we explain some general ideas about the calibration issue of estimator selection methods. We review some known results, putting the emphasis on the concept of minimal penalty which is helpful to design data-driven selection criteria. Secondly we present a new method for bandwidth selection within the framework of kernel density density estimation which is in some sense intermediate between these two main methods mentioned above. We provide some theoretical results which lead to some fully data-driven selection strategy. |
| Databáze: | OpenAIRE |
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