Adaptive and minimax estimation of the cumulative distribution function given a functional covariate
| Autor: | Gaëlle Chagny, Angelina Roche |
|---|---|
| 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), Institut de Mathématiques et de Modélisation de Montpellier (I3M), Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM) |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
Pointwise Adaptive kernel estimator Mathematical optimization Model selection Cumulative distribution function Kernel density estimation Estimator small ball probability Small ball probability [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Minimax Functional random variable [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] Covariate Minimax estimation Conditional cumulative distribution function 62G05 62H12 Statistics Probability and Uncertainty Minimax estimator AMS Subject Classification 2010: 62G05 Mathematics |
| Zdroj: | Electronic Journal of Statistics Electronic Journal of Statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2014, 8 (2), pp.2352-2404. ⟨10.1214/14-EJS956⟩ Electron. J. Statist. 8, no. 2 (2014), 2352-2404 |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/14-EJS956⟩ |
| Popis: | International audience; We consider the nonparametric kernel estimation of the conditional cumulative distribution function given a functional covariate. Given the bias-variance trade-off of the risk, we first propose a totally data-driven bandwidth selection device in the spirit of the recent Goldenshluger-Lepski method and of model selection tools. The resulting estimator is shown to be adaptive and minimax optimal: we establish nonasymptotic risk bounds and compute rates of convergence under various assumptions on the decay of the small ball probability of the functional variable. We also prove lower bounds. Both pointwise and integrated criteria are considered. Finally, the choice of the norm or semi-norm involved in the definition of the estimator is also discussed, as well as the projection of the data on finite dimensional subspaces. Numerical results illustrate the method. |
| Databáze: | OpenAIRE |
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