Bootstrapping the shorth for regression

Author： Durot Cécile   Thiébot Karelle  

Publisher： Edp Sciences

E-ISSN： 1262-3318|10|issue|216-235

ISSN： 1292-8100

Source： ESAIM: Probability and Statistics, Vol.10, Iss.issue, 2006-05, pp. : 216-235

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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 n1/2-rate to a Gaussian law and that the estimator of the centre converges at the n1/3-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.

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