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Pareto Sampling versus Sampford and Conditional Poisson Sampling
Author(s) -
BONDESSON LENNART,
TRAAT IMBI,
LUNDQVIST ANDERS
Publication year - 2006
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2006.00497.x
Subject(s) - mathematics , pareto principle , poisson distribution , estimator , sampling (signal processing) , statistics , conditional probability distribution , poisson sampling , pareto interpolation , sample size determination , conditional probability , sampling design , importance sampling , filter (signal processing) , generalized pareto distribution , slice sampling , monte carlo method , computer science , sociology , computer vision , population , demography , extreme value theory
. Pareto sampling was introduced by Rosén in the late 1990s. It is a simple method to get a fixed size π ps 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.