Bootstrap confidence intervals in nonparametric regression with built-in bias correction

The problem of estimating nonparametric regression with associated confidence intervals is addressed. It is shown that through appropriate choice of infinite order kernel, it is possible to construct bootstrap confidence intervals which do not require either explicit bias correction or suboptimal levels of smoothing at any stage of the estimation. In particular, it is demonstrated that in this setting, consistent estimates are obtained when both the pilot and final smoothings are estimated at the mean square error optimal bandwidth for estimating the regression. The effectiveness of the method is demonstrated through a small simulation study.