On the impact of weights approximation in resampling based on pseudo-populations

The practice of rounding non-integer weights in bootstrapping complex samples from nite populations has been empirically shown to be potentially damaging. Indeed, the extent to which rounding can interfere with basic Bootstrap principles as well as with the formal properties of the nal Bootstrap estimates can be non-negligible and often severe. On the basis of these considerations, in our talk we derive asymptotic results that suggest under which conditions the use of rounding can be detrimental, and attempt a quantication of the unwanted eects induced by this practice with respect to some relevant performance indicators for estimators such as, for example, relative bias and relative root mean square error. Empirical results are discussed based on an extended simulative study, accounting for dierent high-entropy π-ps sampling designs in a number of dierent population scenarios.