Summary
The exact mean square error for the ratio estimator of a finite population total based on simple random sampling without replacement is shown to have an expected value less than that of the variance of the ratio estimator based on Midzuno’s scheme, under a usual super-population model.
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References
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Chaudhuri, A., Adhikary, A.K. On efficiency of the ratio estimator. Metrika 36, 55–59 (1989). https://doi.org/10.1007/BF02614078
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DOI: https://doi.org/10.1007/BF02614078