Bootstrapping the shorth for regression

¹ Université Paris-Sud, Bâtiment 425, 91405 Orsay Cedex, France; cecile.durot@math.u-psud.fr
² Air Pays de la Loire, 2 rue A. Kastler, BP 30723, 44307 Nantes Cedex 3, France. Supported by Air Pays De La Loire

Received: 15 March 2005
Revised: 14 November 2005

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 the length 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 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.