In this paper, we describe a bootstrap method to estimate the bias, the variance and the distribution of the non-parametric Chambers-Dunstan estimator (named the Dorfman-Hall-Chambers-Dunstan (DHCD) estimator) prediction error. Bootstrapping is based on a bootstrap population constructed by sampling the empirical distribution of the superpopulation model recentred residuals. The prediction error of the DHCD estimator is shown to converge to a normal distribution and the consistency of the bootstrap procedure is shown by imitating formally results of the distribution of the prediction error relative to the bootstrap population. Also, the asymptotic form of the optimal bandwidth and a bootstrap estimator of such bandwidth are given for the DHCD estimator. This theory is illustrated by simulation results.†

E-mail: wences@zmat.usc.es‡

E-mail: prada@zmat.usc.es