Pointwise confidence intervals in nonparametric regression with heteroscedastic error structure

We assume a nonparametric model with heteroscedastic error structure and consider pointwise confidence intervals for the mean. We construct them by using quantiles from a Cornish-Fisher expansion and from the wild bootstrap distribution, with as well as without a subsequent bias correction. It turns out that pure undersmoothing, where the Full smoothness is used by the initial estimator, outperforms the method with a subsequent bias correction.