Abstract
Abstract 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.
Highlights
Sampling designs, and sample sizes in particular, are chosen in practice so as to provide reliable estimates for large geographical regions or broad demographic groups
If small area data needs are to be served using survey data there is a need to develop an overall strategy that involves careful attention to satisfy these needs at the planning, sample design and estimation stages of the survey process (Singh et al, 1994)
The aim of this paper is to find the best allocation to strata for a linear combination of the mean squared errors of small area composite estimators and of an overall estimator of the mean, similar to Longford (2006)
Summary
Sample sizes in particular, are chosen in practice so as to provide reliable estimates for large geographical regions or broad demographic groups. Longford (2006) considers the problem of optimal sample sizes for small area estimation for this design. When the overall mean is important Longford does not find an exact or approximate analytical solution to the optimization problem. He suggests that the equation can be solved by numerical methods, such as the Newton method which interpolates between or extrapolates from a pair of provisional solutions, but that solving these equations iteratively may involve a considerable amount of computing when there are thousands of small areas. Longford (2006) did not give an analytical solution when both national (overall) and small area estimates are a priority (G > 0).
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