# Per Gösta Andersson: Conditional Poisson sampling and Pareto sampling: a comparison”

**Time: **
Wed 2019-03-27 13.00 - 14.00

**Location: **
Room B705, Department of Statistics, Stockholm University

**Lecturer: **
Per Gösta Andersson, Department of Statistics

Abstract: In design-based survey sampling theory the finite population quantities are fixed and randomness enters only through the choice of units in the sample. We then look for a sampling design which yields efficient estimation of some population parameter. If auxiliary information is available for the units at the population level, this can be achieved by πps (probability proportional to size) sampling.

Conditional Poisson sampling is carried out by repeated independent Bernoulli trials for all units in the population until the pre-specified sample size n is obtained. Pareto sampling, on the other hand, belongs to the class of order sampling schemes, where the units are first assigned ranking variables generated from standard Pareto distributions. After ordering the units with respect to the realizations of these variables, the sample consists of the units with the n smallest values.

It turns out that conditional Poisson and Pareto sampling are both optimal sampling procedures (and can be combined with the πps technique), but with respect to different criteria. A relevant question is whether the corresponding designs (probability measures) are asymptotically identical.