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Optimal allocation for equal probability two-stage design

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Molefe W.

Statistics in Transition new series

2022

vol. 23

issue 4

129-148

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

An Approximation To The Optimal Subsample Allocation For Small Areas

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Molefe W. B., Shangodoyin D. K., Clark R. G.

Statistics in Transition new series

2015

vol. 16

issue 2

163-182

This paper develops allocation methods for stratified sample surveys in which small area estimation is a priority. We assume stratified sampling with small areas as the strata. Similar to Longford (2006), we seek efficient allocation that minimizes a linear combination of the mean squared errors of composite small area estimators and of an estimator of the overall mean. Unlike Longford, we define mean-squared error in a model-assisted framework, allowing a more natural interpretation of results using an intra-class correlation parameter. This allocation has an analytical form for a special case, and has the unappealing property that some strata may be allocated no sample. We derive a Taylor approximation to the stratum sample sizes for small area estimation using composite estimation giving priority to both small area and national estimation.

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2 Statistics in Transition new series

1 Clark R. G.

1 Molefe W.

1 Molefe W. B.

1 Shangodoyin D. K.

1 2022

1 2015

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Optimal allocation for equal probability two-stage design

An Approximation To The Optimal Subsample Allocation For Small Areas