Exchangeability and the foundations of survey sampling
Exchangeability and the foundations of survey sampling
A new model is proposed for inferences on symmetric functions of a finite population where the only information available is tint the values are exchangeable. Completeness and sufficiency properties of the order statistic are used to give symmetric estimators which become* MWEs. A new subjective justification is therefore found for the use in practice of classical formulae based on simple random sampling, but for any sample design. A superpopulation assumption is not made: such a representation is known not too hold always for finitely exchangeable sequences. The proposed model uses a representation based on the idea of random labelling, and extends the results of the random permutatign approach O.N.K. Rao). Different models are proposed under different assumptions of exchangeability for inferences on functions which are wholly symmetric. For example, the use of classical methods based on stratified random sampling is justified under partial exchangeability, but with respect to the stratification of the assumed model rather than the design.The earlier results are extended for a two-stage population where exchangeability is assumed not only between elements within clusters, but also between clusters of the same size. The optimal estimator is approximated only on average by the commonly used classical estimators under different forms of first-stage sampling.
University of Southampton
1978
Sugden, Roger A
(1978)
Exchangeability and the foundations of survey sampling.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
A new model is proposed for inferences on symmetric functions of a finite population where the only information available is tint the values are exchangeable. Completeness and sufficiency properties of the order statistic are used to give symmetric estimators which become* MWEs. A new subjective justification is therefore found for the use in practice of classical formulae based on simple random sampling, but for any sample design. A superpopulation assumption is not made: such a representation is known not too hold always for finitely exchangeable sequences. The proposed model uses a representation based on the idea of random labelling, and extends the results of the random permutatign approach O.N.K. Rao). Different models are proposed under different assumptions of exchangeability for inferences on functions which are wholly symmetric. For example, the use of classical methods based on stratified random sampling is justified under partial exchangeability, but with respect to the stratification of the assumed model rather than the design.The earlier results are extended for a two-stage population where exchangeability is assumed not only between elements within clusters, but also between clusters of the same size. The optimal estimator is approximated only on average by the commonly used classical estimators under different forms of first-stage sampling.
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Published date: 1978
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Local EPrints ID: 458636
URI: http://eprints.soton.ac.uk/id/eprint/458636
PURE UUID: 4d8a9dc4-59af-4348-8cae-169be61c3a75
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Date deposited: 04 Jul 2022 16:52
Last modified: 04 Jul 2022 16:52
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Author:
Roger A Sugden
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