The choice of smoothing parameter in nonparametric regression through Wild Bootstrap

A bootstrap method to estimate the mean squared error and the smoothing parameter for the multidimensional regression local linear estimator is proposed. This method is based on resampling of the estimated residuals. It uses a bootstrap estimator of the mean squared error to select an asymptotically optimal bandwidth parameter. This is achieved by showing that the mean squared error and its bootstrap estimator are very closed. Thus, the smoothing parameter minimizing the mean squared error is asymptotically close to the smoothing parameter minimizing the bootstrap estimator of the mean squared error. The results are extended to the case in which the response variable contains missing observations. (C) 2003 Elsevier B.V. All rights reserved.