Bootstrap confidence bands in nonparametric regression

In the present paper we construct asymptotic confidence bands in nonparametric regression. Our assumptions admit unequal variances of the observations and nonuniform, possibly considerably clustered design. The confidence band is based on an undersmoothed local linear estimator, and an appropriate quantile is obtained via the wild bootstrap made popular by Härdle and Mammen (1990). We derive certain rates (in the sample size n) for the error in coverage probability, which is an improvement of existing results for methods that rely on the asymptotic distribution of the maximum of some Gaussian process. We propose a practicable rule for a data-dependent choice of the bandwidth.