An estimation of a sensitive attribute by two stage stratified randomized response model

We deal with the estimation of sensitive attribute of the population which is composed of a number of strata by applying stratified sampling to Abdelfatah et al.'s model [1]. We estimate the sensitive parameter in the case of knowing the size of stratum, and check the effect of the proportional allocation method and the optimum allocation method. We extend it to the case of not knowing the size of stratum, and estimate the sensitive parameter by applying stratified double sampling to Abdelfatah et al.'s model [1]. Finally, we compare the efficiency of our suggested estimator to the existing Abdelfatah et al.'s estimator. A practical problem with the use of optimum allocation has been pointed out. Thus, in practice, the use of either proportional allocation or equal allocation has been suggested while estimating proportion of a sensitive attribute using stratified randomized response sampling.