Efficient unequal probability resampling from finite populations

A resampling technique for probability-proportional-to size sampling designs is proposed. It is essentially based on a special form of variable probability, without replacement sampling applied directly to the sample data, yet according to the pseudo-population approach. From a theoretical point of view, it is asymptotically correct: as both the sample size and the population size increase, under mild regularity conditions the proposed resampling design tends to coincide with the original sampling design under which sample data were collected. From a computational point of view, the proposed methodology is easy to be implemented and efficient, because it neither requires the actual construction of the pseudo-population nor any form of randomization to ensure integer weights and sizes. Empirical evidence based on a simulation study1 indicates that the proposed resampling technique outperforms its two main competitors for confidence interval construction of various population parameters including quantiles.