On the role of weights rounding in applications of resampling based on pseudopopulations.

Resampling methods are widely studied and increasinglyemployed in applied research and practice. When deal-ing with complex sampling designs, common resamplingtechniques require adjusting noninteger sampling weightsin order to construct the so called “pseudopopulation” inorder to perform the actual resampling. The practice ofrounding, however, has been empirically shown to beharmful under general designs. In this paper, we presentasymptotic results concerning, in particular, the practiceof rounding resampling weights to the nearest integer, anapproach that is commonly adopted by virtue of its reducedcomputational burden, as opposed to randomization-basedalternatives. We prove that such approach leads to noncon-sistent estimation of the distribution function of the surveyvariable; we provide empirical evidence of the practicalconsequences of the nonconsistency when the point esti-mation of the variance of complex estimators is of interest