Bootstrapping the Chambers–Dunstan estimate of a finite population distribution function

The Chambers–Dunstan estimate of the distribution of a finite population is based on fitting a superpopulation model to the regression of the random variable of interest on a known auxiliary variable. In this paper, the asymptotic distribution of both the Chambers–Dunstan estimate and its bootstrap version are described. The bootstrap performed by resampling a smoothed recentred version of the empirical distribution of the fitting errors is proven to be consistent, and a simulation for which satisfactory results were obtained is described.