On stratified two-stage sampling: Optimum stratification and sample allocation between strata and sampling stages

摘要

Two designs of stratified two-stage sampling are considered in the paper, i.e., the self-weighting design in strata, and the design with fixed sample size from primary sampling units in strata. Two situations are taken into account. In the first one the strata are fixed, and in the second one they have to be constructed. For both designs, formulas for an optimal sample allocation between strata and sampling stages are proposed in the case of fixed strata. Basing on these results, an optimization problem for constructing optimum stratum boundaries in the case of stratified two-stage sampling is given.