Adaptive density estimation in the pile-up model involving measurement errors
| Autor: | Fabienne Comte, Tabea Rebafka |
|---|---|
| Přispěvatelé: | Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Probabilités et Modèles Aléatoires ( LPMA ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Université Paris Diderot - Paris 7 ( UPD7 ) -Centre National de la Recherche Scientifique ( CNRS ) |
| Rok vydání: | 2012 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Statistics::Theory Mathematical optimization fluorescence lifetimes 02 engineering and technology deconvolution Statistics - Applications 01 natural sciences Oracle 010104 statistics & probability [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] 62N01 62G07 0202 electrical engineering electronic engineering information engineering Applications (stat.AP) [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST] 0101 mathematics Mathematics Observational error Nonparametric statistics Estimator 020206 networking & telecommunications biased data projection estimator [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Density estimation [ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH] Multivariate kernel density estimation [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Adaptive nonparametric estimation Deconvolution Statistics Probability and Uncertainty Pile [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR] Algorithm |
| Zdroj: | Electronic journal of statistics Electronic journal of statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2012, 6, pp.2002-2037 Electronic Journal of Statistics Electronic Journal of Statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2012, 6, pp.2002-2037. ⟨10.1214/12-EJS737⟩ Electronic journal of statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2012, 6, pp.2002-2037. 〈10.1214/12-EJS737〉 Electronic journal of statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2012, 6, pp.2002-2037. ⟨10.1214/12-EJS737⟩ Electron. J. Statist. 6 (2012), 2002-2037 Electronic Journal of Statistics, 2012, 6, pp.2002-2037. ⟨10.1214/12-EJS737⟩ |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/12-ejs737 |
| Popis: | Motivated by fluorescence lifetime measurements, this paper considers the problem of nonparametric density estimation in the pile-up model, where observations suffer also from measurement errors. In the pile-up model, an observation is defined as the minimum of a random number of i.i.d. variables following the target distribution. Adaptive nonparametric estimators are proposed for this pile-up model with measurement errors. Furthermore, oracle type risk bounds for the mean integrated squared error (MISE) are provided. Finally, the estimation method is assessed by a simulation study and the application to real fluorescence lifetime data. |
| Databáze: | OpenAIRE |
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