On Chao's unequal probability sampling plan
S. Sengupta · Biometrika · 1989
We give necessary and sufficient conditions for the second-order inclusion probabilities to be strictly positive under Chao's (1982) sampling plan for some order of arrangement of the population units. We also prove that the variance of the Horvitz–Thompson estimator of the population total based on this sampling plan is smaller than the variance of the Hansen–Hurwitz estimator based on a probability proportional to size with replacement sample involving the same number of draws.