Generalized exponential type estimator for the mean of sensitive variable in the presence of non-sensitive auxiliary variable

We proposed a generalized two stage optional randomized response model by single sample approach and developed a generalized exponential type estimator for the mean of sensitive variable using information from a non-sensitive auxiliary variable. Privacy protection and some special cases for the suggested model has also been discussed. Simulation and numerical study are carried out to assess the performance of the suggested estimator. We compare the proposed model with some existing estimators and conclude that our proposed model is more efficient under certain conditions.

Automated summary

In this study, a generalized two-stage optional randomized response model was proposed using a single sample approach. A generalized exponential type estimator was developed for the mean of a sensitive variable, utilizing information from a non-sensitive auxiliary variable. Privacy protection and special cases of the suggested model were discussed, and simulation and numerical studies were conducted to assess the performance of the suggested estimator. The proposed model was compared with existing estimators, showing that it is more efficient under specific conditions.