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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.

MSC:
 62D05 Sampling theory, sample surveys
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References:
 [1] Adhikary AK, Chaudhuri A, Vijayan K (1984) Optimum sampling strategies for randomized response trials. Internat Statist Rev 52:115–125 · Zbl 0579.62007 [2] Eriksson SA (1973) A new model for randomized response. Internat Statist Rev 41:101–113 · Zbl 0287.92008 [3] Liu TP (1974) A general unbiased estimator for the variance of a finite population. Sankhya Sr C 36:23–32 · Zbl 0299.62009 [4] Sengupta S, Kundu D (1989) Estimation of finite population mean in randomized response surveys. J Statist Plan Inf 23:117–125 · Zbl 0685.62015 [5] Warner SL (1965) Randomized response – A survey technique for eliminating evasive answer bias. J Amer Statist Assoc 60:63–69 · Zbl 1298.62024
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