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Admissible unbiased variance estimation in finite population sampling under randomized response. (English) Zbl 0738.62007
Summary: Let \(P\) 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 of \(P\) and (ii) an unbiased estimator of the population variance \(P(1-P)\), based on an arbitrary but fixed sampling design, under the randomized response plans due to S. L. Warner [J. Am. Stat. Assoc. 60, 63-69 (1965)] and S. A. Eriksson [Internat. statist. Review 41, 101-113 (1973; Zbl 0287.92008)]. Admissibility of an unbiased strategy for estimating the population variance is also established.

62D05 Sampling theory, sample surveys
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