Summary
Koop [1967] proved that interpenetrating samples of unequal sizes are more efficient than those with equal sizes for estimating a finite population total. After observing that there is a serious lacuna present in his proof, a correct proof has been suggested. The optimum choice of individual sample sizes has also been discussed for a given (i) total sample size, (ii) cost and (iii) precision, with an assumed cost structure. Finally, the resulting estimators have been compared with those based on a single sample.
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Sengupta, S. On interpenetrating samples of unequal sizes. Metrika 29, 175–188 (1982). https://doi.org/10.1007/BF01893377
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DOI: https://doi.org/10.1007/BF01893377