Probability Proportional to Size (PPS) Sampling

Abstract Probability proportional to size (PPS) sampling is a method of sampling from a finite population in which a size measure is available for each population unit before sampling and where the probability of selecting a unit is proportional to its size. Its use arises in two particular contexts: (i) multistage sampling and (ii) single‐stage sampling of establishments. Unbiased estimation is obtained using the Hansen–Hurvitz estimator in the case of PPS with replacement sampling and the Horvitz–Thompson estimator in the case of probability proportional to size without replacement (PPSWOR) sampling. Variance estimation is also discussed. A variety of PPSWOR designs are outlined, including systematic sampling and conditional Poisson sampling.