[Statlist] Séminaires de Statistique - Institut de Statistique - Université de Neuchâtel

[KONDYLIS Atanassios]

Séminaires de Statistique 
Mardi 15 novembre 2005 à 11h00 
Institut de Statistique, Université de Neuchâtel 
Espace de l'Europe 4, Neuchâtel
http://www2.unine.ch/statistics

Lennart Bondesson, Umeå, Sweden 

Pareto Sampling versus Sampford and Conditional Poisson Sampling

Abstract. Pareto sampling was introduced by Rosén in the late 1990s. It is a simple method to get a fixed size \pi 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 samples appears as a by-product. Further, it is shown how the inclusion probabilities of all orders for the Pareto design can be calculated from those of the conditional Poisson design. A new explicit accurate approximation of the 2nd order inclusion probabilities, valid for several designs, is presented and applied to get variance estimates of the Horvitz-Thompson estimator of the single sum type.  
 
Key words: acceptance-rejection, conditional Poisson sampling,  Horvitz-Thompson estimator, inclusion probabilities, Laplace approximation, 
Pareto sampling, \pi ps sample, Sampford sampling, variance estimation


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