Estimation of mean of a sensitive variable using efficient exponential-type estimators in stratified sampling

Sousa et al. [Improved mean estimation of a sensitive variable using auxiliary information in stratified sampling. J Stat Manage Syst. 2014;17(5-6):503-518] presented a ratio estimator for mean estimation in stratified sampling using an additive scrambled response model for a sensitive variable. In order to improve the estimation of mean, this study is motivated to introduce two difference-cum-exponential ratio estimators for mean estimation of a sensitive variable in stratified sampling. The theoretical discussion is presented to show that the two proposed estimators are more efficient than the available estimators including Sousa et al. [Improved mean estimation of a sensitive variable using auxiliary information in stratified sampling. J Stat Manage Syst. 2014;17(5-6):503-518] ratio and regression estimator in certain situations. A real-life application and simulation studies are presented to express the performance of the proposed estimator and existing estimators. The two studies provide evidence that the two proposed estimators perform more efficiently for mean estimation than the other available estimators.