On the role of weights rounding in applications of resampling based on pseudo-populations

Resampling methods are widely studied and increasingly employed in applied research and practice. When dealing with complex sampling designs, common resampling techniques require to adjust non-integer sampling weights in order to construct the so called “pseudo-population” where to perform the actual resampling. In particular, to lighten the computational burden, it is commonly suggested to round resampling weights to the nearest integer. This practice, however, has been empirically shown to be harmful under general designs. Here we develop theoretical support for this fact, and present asymptotic results concerning the bias induced by the rounding practice.