Construction of automatic confidence intervals in nonparametric heteroscedastic regression by a moment-oriented bootstrap

We construct pointwise confidence intervals for regression functions. The method uses nonparametric kernel estimates and the moment-oriented bootstrap method of Bunke which is a wild bootstrap based on smoothed local estimators of higher order error moments. We show that our bootstrap consistently estimates the distribution of mh(x0) - m(xo). In the present paper we focus on fully data-driven procedures and prove that the confidence intervals give asymptotically correct coverage probabilities.