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

Area of Science:

• Statistics
• Survey Methodology
• Data Privacy

Background:

• Estimating sensitive information accurately is challenging.
• Existing randomized response techniques (RRT) have limitations in efficiency and privacy.
• Auxiliary variables can potentially improve RRT models.

Purpose of the Study:

• Introduce novel calibrated randomized response techniques (C-ORRT) models.
• Enhance the efficiency, stability, and robustness of RRT models.
• Improve the estimation of sensitive information while maintaining privacy.

Main Methods:

• Modified existing RRT models using calibration with auxiliary variables.
• Derived theoretical properties including estimators, variances, and privacy levels.
• Developed a combined metric for efficiency and privacy assessment.

Main Results:

• C-ORRT models demonstrated lower biases and reduced variances.
• Achieved higher relative efficiency and enhanced privacy levels.
• Showcased superior performance in a combined metric of variance and privacy.

Conclusions:

• The proposed C-ORRT models are more efficient, stable, and robust than existing RRT models.
• C-ORRT models offer a superior approach for sensitive data estimation.
• Numerical applications validated the theoretical advantages of C-ORRT models.