Automatic bandwidth choice and confidence intervals in nonparametric regression

In the present paper we combine the issues of bandwidth choice and construction of confidence intervals in nonparametric regression. Main emphasis is put on fully data-driven methods. We modify the root n-consistent bandwidth selector of Hardle, Hall and Marron such that it is appropriate for heteroscedastic data, and we show how one can optimally choose the bandwidth g of the pilot estimator <(m)over cap(g)>. Then we consider classical confidence intervals based on kernel estimators with data-driven bandwidths and compare their coverage accuracy. We propose a method to put undersmoothing with a data-driven bandwidth into practice and show that this procedure outperforms explicit bias correction.