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. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..
Asymptotic distances between probability distributions appearing in πps sampling theory are studied. The distributions are Poisson, Conditional Poisson (CP), Sampford, Pareto, Adjusted CP and Adjusted Pareto sampling. We start with the Kullback-Leibler divergence and the Hellinger distance and derive a simpler distance measure using a Taylor expansion of order two. This measure is evaluated first theoretically and then numerically, using small populations. The numerical examples are also illustrated using a multidimensional scaling technique called principal coordinate analysis (PCO). It turns out that Adjusted CP, Sampford, and adjusted Pareto are quite close to each other. Pareto is a bit further away from these, then comes CP and finally Poisson which is rather far from all the others.
We present a construction of cyclically permutable codes using cyclic codes. This construction is a generaliiation and unification of several other constructions. The codes are in a certain sense better than, or equally good as, codes from other constructions using the same technique.
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