Optimal Allocation for Equal Probability Two-Stage Design

Molefe, Wilford

doi:10.2478/stattrans-2022-0046

Author

Molefe Wilford (University of Botswana, Botswana)

Title

Optimal Allocation for Equal Probability Two-Stage Design

Source

Statistics in Transition, 2022, vol. 23, nr 4, s. 129-148, tab., bibliogr. 13 poz.

Keyword

Estymacja, Estymatory, Metody estymacji, Metody statystyczne
Estimation, Estimators, Estimation methods, Statistical methods

Note

summ.

Abstract

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. (original abstract)

Accessibility

The Main Library of the Cracow University of Economics
The Library of Warsaw School of Economics
The Library of University of Economics in Katowice

Full text

Bibliography

Bankier, M. D., (1988). Power allocations: determining sample sizes for subnational areas. The American Statistician, 42(3), pp. 174-177.
Clark, R. G., Steel, D. G., (2007). Sampling within households in households surveys. Journal of the Royal Statistical Society A, 170(Issue 1), pp. 63-82.
Cochran, W. G., (1977). Sampling Techniques. Wiley and Sons.
Foreman, E. K., (1991). Survey Sampling Principles. Marcel Dekker, Inc.
Fuller, W. A., (1999). Environmental Surveys Over Time. Journal of Agricultural, Biological and Environmental Statistics, 4, pp. 331-345.
Hansen, M. H., Hurwitz, W. N., and Madow, W. G., (1953). Sample survey methods and theory, volume 1 & 2. Wiley, New York.
Hidiroglou, M. A., Patak, Z., (2004). Domain estimation using linear regression. Survey Methodology, 30, pp. 67-78.
Longford, N. T., (2006). Sample size calculation for small-area estimation. Survey Methodology, 32(1), pp. 87-96.
Molefe, W. B., (2011). Sample design for small area estimation. PhD thesis, University of Wollongong, http://ro.uow.edu.au/theses/3495.
Molefe, W. B., Clark, R. G., (2015). Model-assisted optimal allocation for planned domains using composite estimation. Survey Methodology, 41(2), pp. 377387.
Molefe, W. B., Shangodoyin, D. K., and Clark, R. G., (2015). An approximation to the optimal subsample allocation for small areas. Statistics in Transition, new series, 16(2), pp. 163-182.
Pettersson, H., Sisouphanthong, B., (2005). Household Sample Surveys in Developing and Transition Countries, chapter Cost Model for an Income and Expenditure Survey, pages 267-277. Number 96 in Series F. United Nations: Statistics Division, Department of Economic and Social Affairs.
Sukhatme, P. V., Sukhatme, B. V., Sukhatme, S., and Asok, C., (1954). Sampling theory of surveys with applications. Iowa State University Press, third edition.

Cited by

ISSN

1234-7655

Language

eng

URI / DOI

BazEkon - The Main Library of the Cracow University of Economics

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