Sampling and maintenance of a stratified panel of fixed size - ARCHIVED

Statistical agencies often constitute their business panels by Poisson sampling, or by stratified sampling of fixed size and uniform probabilities in each stratum. This stampling corresponds to algorithms which use permanent numbers following a uniform distribution. Since the characteristics of the units change over time, it is necessary to periodically conduct resamplings while endeavouring to conserve the maximum number of units. The solution by Poisson sampling is the simplest and provides the maximum theoretical coverage, but with the disadvantage of a random sample size. On the other hand, in the case of stratified sampling of fixed size, the changes in strata cause difficulties precisely because of these fixed size constraints. An initial difficulty is that the finer the stratification, the more the coverage is decreased. Indeed, this is likely to occur if births constitute separate strata. We show how this effect can be corrected by rendering the numbers equidistant before resampling. The disadvantage, a fairly minor one, is that in each stratum the sampling is no longer a simple random sampling, which makes the estimation of the variance less rigorous. Another difficulty is reconciling the resampling with an eventual rotation of the units in the sample. We present a type of algorithm which extends after resampling the rotation before resampling. It is based on transformations of the random numbers used for the sampling, so as to return to resampling without rotation. These transformations are particularly simple when they involve equidistant numbers, but can also be carried out with the numbers following a uniform distribution.