| Title:
|
One Bootstrap suffices to generate sharp uniform bounds in functional estimation (English) |
| Author:
|
Deheuvels, Paul |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
47 |
| Issue:
|
6 |
| Year:
|
2011 |
| Pages:
|
855-865 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\mathbb{R}$. (English) |
| Keyword:
|
nonparametric functional estimation |
| Keyword:
|
density estimation |
| Keyword:
|
regression estimation |
| Keyword:
|
bootstrap |
| Keyword:
|
resampling methods |
| Keyword:
|
confidence regions |
| Keyword:
|
empirical processes |
| MSC:
|
62G05 |
| MSC:
|
62G08 |
| MSC:
|
62G09 |
| MSC:
|
62G15 |
| MSC:
|
62G20 |
| MSC:
|
62G30 |
| idZBL:
|
Zbl 06047590 |
| idMR:
|
MR2907846 |
| . |
| Date available:
|
2011-12-08T09:59:21Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141729 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| . |
