Summary
After a review of the literature and preliminaries in sections 1 and 2. the essentials of an estimation theory for sample surveys, which takes into account measurement and/or response errors, are given in section 3. There it is shown that the linear estimator with the lesst mean square error does not exist; an unattained lower bound to the mean square error is established. Section 4 shows that estimates of variance of linear estimators in standard theory are always negatively biased. Finally, the method of independent replication and its use for the purpose of estimating variance is discussed in section 5.
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Koop, J.C. Notes for a unified theory of estimation for sample surveys taking into account response erros. Metrika 21, 19–39 (1974). https://doi.org/10.1007/BF01893890
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DOI: https://doi.org/10.1007/BF01893890