The first-order autoregression model with heteroskedastic innovations is considered and it is shown that the classical bootstrap procedure based on estimated residuals fails for the least-squares estimator of the autoregression coefficient. A different procedure called wild bootstrap, respectively its modification is considered and its consistency in the strong sense is established under very mild moment conditions.
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...