An efficient estimation framework for sensitive data under randomized response with real-world applications

Abstract Accurate estimation of sensitive characteristics in radiation-related studies is often affected by response bias and non-cooperation, leading to unreliable statistical inference. The Randomized Response Technique (RRT) offers an effective mechanism to mitigate such issues by preserving respondent confidentiality while enhancing data reliability. In this study, we develop an improved class of transformed ratio estimator for estimating the finite population mean of sensitive variables by incorporating auxiliary information within the RRT framework. The statistical properties of the proposed estimator developed to improve the estimation of population parameters in the presence of sensitive characteristics including bias and mean squared error (MSE), are derived using first-order approximations. A theoretical efficiency comparison with existing estimators is conducted to establish its superiority under defined conditions. To demonstrate practical applicability, the methodology is validated using a publicly available solar ultraviolet (UV) radiation dataset obtained from Kaggle, along with a supporting dataset on student depression. The empirical results indicate that the proposed estimator consistently outperforms traditional estimators in terms of reduced MSE and enhanced efficiency. The findings underscore the importance of robust estimation techniques in radiation research, particularly in studies involving sensitive attributes where data accuracy and respondent privacy are critical.