Calibrated optional randomized response techniques for efficient and robust estimation of quantitative sensitive variables

This paper introduced new classes of calibrated randomized response techniques (C-ORRT) models aimed at estimating sensitive information. The proposed C-ORRT models were developed by modifying existing RRT models using auxiliary variable through calibration methods. The goal was to develop RRT models that are more efficient, stable, and robust than the current options. The theoretical properties such as estimators, variances, privacy levels, and a combined metric for efficiency and privacy to assess the robustness and applicability of the proposed models were derived. The theoretical efficiency conditions of the C-ORRT models were established in comparison to some existing RRT models. Numerical applications using both real and simulated data supported the theoretical findings, demonstrating that the C-ORRT models exhibited lower biases, reduced variances, higher relative efficiency, enhanced privacy levels, and a better combined metric of variance and privacy. This indicates the superiority of the C-ORRT models over existing RRT models.