One bootstrap suffices to generate sharp uniform bounds in functional estimation

Title:

One bootstrap suffices to generate sharp uniform bounds in functional estimation

Creator:

Deheuvels, Paul

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a9df6c3d-5ad0-4469-b190-97e521b99806
uuid:a9df6c3d-5ad0-4469-b190-97e521b99806

Subject:

nonparametric functional estimation, density estimation, regression estimation bootstrap, resampling methods, confidence regions, and empirical processes

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 <span class="tex"><b>I</b></span>, 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 <span class="tex"><b>I</b></span> 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 <b>R</b>.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[855]-865

Source:

Kybernetika | 2011 Volume:47 | Number:6

Harvested from:

CDK

Metadata only:

false