Pareto sampling versus Sampford and Conditional Poisson sampling
2006 (English)In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 33, no 4, 699-720 p.Article in journal (Refereed) Published
Pareto sampling was introduced by Rosén in the late 1990s. It is a simple method to get a fixed size πps sample though with inclusion probabilities only approximately as desired. Sampford sampling, introduced by Sampford in 1967, gives the desired inclusion probabilities but it may take time to generate a sample. Using probability functions and Laplace approximations, we show that from a probabilistic point of view these two designs are very close to each other and asymptotically identical. A Sampford sample can rapidly be generated in all situations by letting a Pareto sample pass an acceptance–rejection filter. A new very efficient method to generate conditional Poisson (CP) samples appears as a byproduct. Further, it is shown how the inclusion probabilities of all orders for the Pareto design can be calculated from those of the CP design. A new explicit very accurate approximation of the second-order inclusion probabilities, valid for several designs, is presented and applied to get single sum type variance estimates of the Horvitz–Thompson estimator.
Place, publisher, year, edition, pages
Wiley InterScience , 2006. Vol. 33, no 4, 699-720 p.
acceptance–rejection, conditional Poisson sampling, Horvitz–Thompson estimator, inclusion probabilities, Laplace approximation, Pareto sampling, πps sample, Sampford sampling, variance estimation
Probability Theory and Statistics
Research subject Mathematical Statistics
IdentifiersURN: urn:nbn:se:umu:diva-7839DOI: 10.1111/j.1467-9469.2006.00497.xOAI: oai:DiVA.org:umu-7839DiVA: diva2:147510