Allocation of Sample Size in Stratified Sampling: Under Superpopulation Models

The problem of allocation of sample size to strata is considered for various stratified sampling strategies including stratified SRSWR and SRSWOR designs along with unbiased expansion, separate and combined ratio estimators, PPSWR sampling strategy under different superpopulation models. Optimum allocation is derived under an appropriate superpopulation model and model optimum allocation is obtained along with validating condition. Approximate allocations are derived with various approximations and finally two generalised allocations are obtained specially in case of SRS designs under the assumption of equal stratum coefficient of variation (ESCV). Several particular cases are also deduced and Hanurav?s & Rao?s allocations follow as special cases. The results are empirically illustrated with several live populations. The applications and implications of the condition and ESCV assumption are explored and usefulness of the condition is empirically established for choosing the best possible allocation for use in practice at the planning stage of a survey.