Privacy-accuracy trade-off optimization in sensitive surveys through regression estimation

Collecting reliable information on sensitive quantitative characteristics remains a big challenge in social and behavioral surveys, as respondents often hesitate to answer truthfully. The Randomized Response Technique (RRT) helps protect privacy, but many existing models do not balance privacy and efficiency well. To resolve this problem, this study proposes a novel regression estimator designed to accurately estimate the sensitive population mean. The strength of this approach lies in incorporating non-sensitive auxiliary variables into data collected under strict privacy protocols. To thoroughly evaluate the behavior of this estimator, we apply it to data collected through existing distinct randomized response models. Theoretically, the proposed regression estimator is unbiased and benefits from a straightforward, closed-form variance expression, allowing for practical application. We assess privacy protection using a deviation-based metric, while efficiency is assessed through in terms of sampling variance. To capture the overall performance of the models, we also employ unified, weighted, and log-weighted composite measures that balance both privacy and precision. Extensive numerical examples and Monte Carlo simulations demonstrate that the proposed estimator usually has lower variance and offers a better balance between privacy and efficiency than other existing mean estimators. These results indicate that the proposed estimator provides a practical, efficient, and privacy-preserving tool for surveys involving sensitive quantitative data.