Abstract
LetP be the proportion of units in a finite population possessing a sensitive attribute. We prove the admissibility of (i) an unbiased estimator of the variance of a general homogeneous linear unbiased estimator ofP and (ii) an unbiased estimator of the population varianceP(1−P), based on an arbitrary but fixed sampling design, under the randomized response plans due to Warner (1965) and Eriksson (1973). Admissibility of an unbiased strategy for estimating the population variance is also established.
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References
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Sengupta, S., Kundu, D. Admissible unbiased variance estimation in finite population sampling under randomized response. Metrika 38, 71–82 (1991). https://doi.org/10.1007/BF02613600
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DOI: https://doi.org/10.1007/BF02613600