Stratified balanced sampling - ARCHIVED

In the selection of a sample, a current practice is to define a sampling design stratified on subpopulations. This reduces the variance of the Horvitz-Thompson estimator in comparison with direct sampling if the strata are highly homogeneous with respect to the variable of interest. If auxiliary variables are available for each individual, sampling can be improved through balanced sampling within each stratum, and the Horvitz-Thompson estimator will be more precise if the auxiliary variables are strongly correlated with the variable of interest. However, if the sample allocation is small in some strata, balanced sampling will be only very approximate. In this paper, we propose a method of selecting a sample that is balanced across the entire population while maintaining a fixed allocation within each stratum. We show that in the important special case of size-2 sampling in each stratum, the precision of the Horvitz-Thompson estimator is improved if the variable of interest is well explained by balancing variables over the entire population. An application to rotational sampling is also presented.