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Bootstrapping the shorth for regression

Published online by Cambridge University Press:  03 May 2006

Cécile Durot  and
Karelle Thiébot
Cécile Durot
Affiliation:
Université Paris-Sud, Bâtiment 425, 91405 Orsay Cedex, France; [email protected]
Karelle Thiébot
Affiliation:
Université Paris-Sud, Bâtiment 425, 91405 Orsay Cedex, France; [email protected] Air Pays de la Loire, 2 rue A. Kastler, BP 30723, 44307 Nantes Cedex 3, France. Supported by Air Pays De La Loire
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Abstract

The paper is concerned with the asymptotic distributions of estimators for the length and the centre of the so-called η-shorth interval in a nonparametric regression framework. It is shown that the estimator of thelength converges at the n 1/2-rate to a Gaussian law and that the estimator of the centre converges at the n 1/3-rate to the locationof the maximum of a Brownian motion with parabolic drift.Bootstrap procedures are proposed and shown to be consistent. They are compared with the plug-in method through simulations.

Keywords

Brownian motion with parabolic driftbootstraplocation of maximumshorth.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 10 , February 2006 , pp. 216 - 235
Copyright
© EDP Sciences, SMAI, 2006

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