an:00009074
Zbl 0738.62007
Sengupta, S.; Kundu, D.
Admissible unbiased variance estimation in finite population sampling under randomized response
EN
Metrika 38, No. 2, 71-82 (1991).
0026-1335 1435-926X
1991
j
62D05
finite population; population variance; fixed sampling design; randomized response plans; unbiased estimator of the variance of a general homogeneous linear unbiased estimator
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 \textit{S. L. Warner} [J. Am. Stat. Assoc. 60, 63-69 (1965)] and \textit{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.
0287.92008