For a comparison between the efficiencies of the ratio estimator and the randomized PPS
estimator, the reader is referred to Foreman and Brewer (1971), Cochran (1977) and the references given therein. A
drawback of these comparisons is that finite populations corrections are ignored. Hartley and Rao (1962) take the
finite population correction into account but without an explicit formula for the efficiency. Elaborating on the results
of Gabler (1984), Qualité (2008) shows that the related HT estimator from a rejective Poisson sample of size n is more
efficient than the Hansen-Hurwitz estimator for a sampling scheme with replacement. No formula for the increased
efficiency is given, however