Estimation of a rare sensitive attribute in two-stage sampling using a randomized response model under Poisson distribution

ABSTRACT Unbiased estimation procedures of the mean total number of persons with a rare sensitive attribute apply for a clustered population under two-stage and stratified two-stage sampling schemes. Randomized response model is used to obtain the estimators, when the parameter of an unrelated rare non-sensitive attribute is either known or unknown. The variances of the resultant estimators are derived and their unbiased estimates are expressed. Numerical comparisons show that dispersions in the estimates are lower than other contemporary estimators.