Geodesic
One Bootstrap suffices to generate sharp uniform bounds in functional estimation
Kybernetika, Tome 47 (2011) no. 6, pp. 855-865.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We consider, in the framework of multidimensional observations, nonparametric functional estimators, which include, as special cases, the Akaike–Parzen–Rosenblatt kernel density estimators ([1, 18, 20]), and the Nadaraya–Watson kernel regression estimators ([16, 22]). We evaluate the sup-norm, over a given set ${\bf I}$, of the difference between the estimator and a non-random functional centering factor (which reduces to the estimator mean for kernel density estimation). We show that, under suitable general conditions, this random quantity is consistently estimated by the sup-norm over ${\bf I}$ of the difference between the original estimator and a bootstrapped version of this estimator. This provides a simple and flexible way to evaluate the estimator accuracy, through a single bootstrap. The present work generalizes former results of Deheuvels and Derzko [4], given in the setup of density estimation in $\mathbb{R}$.
Classification : 62G05, 62G08, 62G09, 62G15, 62G20, 62G30
Keywords: nonparametric functional estimation; density estimation; regression estimation; bootstrap; resampling methods; confidence regions; empirical processes 
@article{KYB_2011__47_6_a3,
     author = {Deheuvels, Paul},
     title = {One {Bootstrap} suffices to generate sharp uniform bounds in functional estimation},
     journal = {Kybernetika},
     pages = {855--865},
     publisher = {mathdoc},
     volume = {47},
     number = {6},
     year = {2011},
     mrnumber = {2907846},
     zbl = {06047590},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011__47_6_a3/}
}
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Deheuvels, Paul. One Bootstrap suffices to generate sharp uniform bounds in functional estimation. Kybernetika, Tome 47 (2011) no. 6, pp. 855-865. http://geodesic.mathdoc.fr/item/KYB_2011__47_6_a3/