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.
