Optimal sample allocation for the Stratified Simple Random Sam- pling and the Incomplete Stratified Sampling design

A sampling design widely adopted in official statistics is the Stratified Simple Random Sampling (SSRS) design in which strata are defined by crossing of the variables that define the domains of estimate. When there are many strata, the SSRS design could be inefficient. We propose an alternative sampling design denoted as Incomplete Stratified Sampling (ISS) design. The design exploits all the potential auxiliary information available both from the sampling frame and from other sources such as previous surveys in a more efficient way with respect to the traditional SSRS design. The ISS design enable to fix the sample size for the each estimation domain obtaining the required precisions for the sample estimates, achieving a reduction of the overall sample size with respect to the SSRS design since for the latter the allocation process has no constraints on stratum sample sizes.