The pseudo-population bootstrap approach in survey sampling consists of constructing a pseudo-population from the sampled units and to obtain a bootstrap sample using the survey design, see e.g. Booth et al. (1994). In an i.i.d. context, Hall, DiCiccio and Romano (1989) have shown that smoothing the empirical distribution function from which bootstrap samples are taken can improve variance estimates of quantile estimators.
In this paper, we extend the smooth bootstrap to the survey sampling setting. The method consists of adding i.i.d. N(0,h^2) random variables to each unit of the pseudo-population. We study the performance of the approach to construct variance estimates and confidence intervals, notably for quantile estimators. As is usually the case with smoothing methods, special care is given to the choice of the bandwidth h.