Efficient estimation of population variance of a sensitive variable using a new scrambling response model

Area of Science:

• Statistics
• Survey Methodology
• Data Privacy

Background:

• Handling sensitive variables in surveys presents significant challenges.
• Existing variance estimation techniques may not adequately protect respondent privacy.
• The need for robust models that balance data utility and privacy is critical.

Purpose of the Study:

• To introduce a novel scrambling response model for sensitive variables.
• To develop a generalized estimator for variance estimation using auxiliary information.
• To evaluate the privacy protection and statistical performance of the proposed model.

Main Methods:

• Development of a pioneering scrambling response model.
• Formulation of a generalized estimator utilizing two auxiliary information sources.
• Derivation of analytical expressions for bias and mean square error (MSE).
• Conducting simulation experiments and empirical analyses.

Main Results:

• The proposed generalized estimator demonstrates minimal mean square error (MSE).
• The estimator outperforms existing techniques under scrambling response models.
• The study provides a robust evaluation of privacy protection levels.

Conclusions:

• The novel scrambling response model and generalized estimator offer enhanced statistical performance.
• The proposed method provides superior privacy protection for respondents.
• This approach advances techniques for handling sensitive data in statistical surveys.