Optimal allocation for equal probability two-stage design

Abstract This paper develops optimal designs when it is not feasible for every cluster to be represented in a sample as stratified design, by assuming equal probability two-stage sampling where clusters are small areas. The allocation methods surveys small-area estimates priority. We seek efficient allocations the aim minimize linear combination of mean squared errors composite area estimators and an estimator overall mean. suggest some alternative with view minimizing same objective. Several alternatives, including area-only found perform nearly well but better practical properties. Designs evaluated numerically using Switzerland canton data Botswana administrative districts data.