Minimum variance stratification of a finite population
Minimum variance stratification of a finite population
This paper considers the combined problem of allocation and stratification in order to minimise the variance of the expansion estimator of a total, taking into account that the population is finite. The proof of necessary minimum variance conditions utilises the Kuhn-Tucker Theorem. Stratified simple random sampling with non-negligible sampling fractions is an important design in sample surveys. We go beyond limiting assumptions that have often been used in the past, such as that the stratification equals the study variable or that the sampling fractions are small. We discuss what difference the sampling fractions will make for stratification. In particular, in many surveys the sampling fraction equals one for some strata. The main theorem of this paper is applied to two populations with different characteristics, one of them being a business population and the other one a small population of 284 Swedish municipalities. We study empirically the sensitivity of deviations from the optimal solution.
Southampton Statistical Sciences Research Institute, University of Southampton
Hedlin, Dan
0209f71c-a071-4fde-8c2d-d3e7cedaf611
2003
Hedlin, Dan
0209f71c-a071-4fde-8c2d-d3e7cedaf611
Hedlin, Dan
(2003)
Minimum variance stratification of a finite population
(S3RI Methodology Working Papers, M03/07)
Southampton, UK.
Southampton Statistical Sciences Research Institute, University of Southampton
30pp.
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Monograph
(Working Paper)
Abstract
This paper considers the combined problem of allocation and stratification in order to minimise the variance of the expansion estimator of a total, taking into account that the population is finite. The proof of necessary minimum variance conditions utilises the Kuhn-Tucker Theorem. Stratified simple random sampling with non-negligible sampling fractions is an important design in sample surveys. We go beyond limiting assumptions that have often been used in the past, such as that the stratification equals the study variable or that the sampling fractions are small. We discuss what difference the sampling fractions will make for stratification. In particular, in many surveys the sampling fraction equals one for some strata. The main theorem of this paper is applied to two populations with different characteristics, one of them being a business population and the other one a small population of 284 Swedish municipalities. We study empirically the sensitivity of deviations from the optimal solution.
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Published date: 2003
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Local EPrints ID: 7796
URI: http://eprints.soton.ac.uk/id/eprint/7796
PURE UUID: 938eb239-5105-44cc-97b9-a4ce86330b47
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Date deposited: 07 Jun 2004
Last modified: 15 Mar 2024 04:48
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Author:
Dan Hedlin
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