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A general scrambled randomized response model that aims to regulate a realistic swapping between efficiency and privacy protection is developed. The basic initiative is to offer a hotchpotch of many different scrambling randomized response models, including many existing additive, subtractive, multiplicative and general scrambling randomized response models. A more efficient and generalized class of estimators for estimating the population mean based on two non-sensitive auxiliary variables is employed using the general scrambling randomized response model. The bias and mean square error of all estimators are computed from a simulation, along with empirical studies by assuming the additive model, multiplicative model and proposed generalized scrambled model in separate tables. The simulation and empirical results demonstrate that the proposed estimators are more efficient than the existing ones. It is also shown that the gain in efficiency is higher when the proposed model is used.

Efficient class of estimators for the estimation of the mean of a sensitive variable using multi-auxiliary variables