Bootstrapping the shorth for regression
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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.
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