Adaptive nonparametric estimation of a component density in a two-class mixture model
| Autor: | Hoang, Van Ha, Chagny, Gaëlle, Channarond, Antoine, Hoang, Van, Roche, Angelina |
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| Přispěvatelé: | Laboratoire de Mathématiques Raphaël Salem (LMRS), Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), 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), RIN AStERiCs 17B01101GR, ANR-18-CE40-0014,SMILES,Modélisation et Inférence Statistique pour l'Apprentissage non-supervisé à partir de Données Massives(2018), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Pointwise [STAT.AP]Statistics [stat]/Applications [stat.AP] Smoothness (probability theory) 62G07 62G20 Applied Mathematics 05 social sciences Nonparametric statistics Estimator Probability density function Mathematics - Statistics Theory [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Statistics Theory (math.ST) Mixture model 01 natural sciences 010104 statistics & probability Quadratic equation Kernel (statistics) 0502 economics and business FOS: Mathematics Applied mathematics 0101 mathematics Statistics Probability and Uncertainty 050205 econometrics Mathematics |
| Zdroj: | Journal of Statistical Planning and Inference Journal of Statistical Planning and Inference, Elsevier, 2021, 216, ⟨10.1016/j.jspi.2021.05.004⟩ |
| ISSN: | 0378-3758 1873-1171 |
| DOI: | 10.48550/arxiv.2007.15518 |
| Popis: | International audience; A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly weighted kernel estimator with a fully data-driven bandwidth selection method, in the spirit of the Goldenshluger and Lepski method. An oracle-type inequality for the pointwise quadratic risk is derived as well as convergence rates over Hölder smoothness classes. The theoretical results are illustrated by numerical simulations. |
| Databáze: | OpenAIRE |
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