Volume 10, September 2006
|Page(s)||216 - 235|
|Published online||03 May 2006|
Bootstrapping the shorth for regression
Université Paris-Sud, Bâtiment 425, 91405 Orsay Cedex, France; email@example.com
2 Air Pays de la Loire, 2 rue A. Kastler, BP 30723, 44307 Nantes Cedex 3, France. Supported by Air Pays De La Loire
Revised: 14 November 2005
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 the length converges at the n1/2-rate to a Gaussian law and that the estimator of the centre converges at the n1/3-rate to the location of 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.
Mathematics Subject Classification: 62E20 / 62G05 / 62G08 / 62G09
Key words: Brownian motion with parabolic drift / bootstrap / location of maximum / shorth.
© EDP Sciences, SMAI, 2006
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