GENERALIZED EXPONENTIAL ESTIMATORS FOR POPULATION VARIANCE USING RANDOMIZED RESPONSE MODEL

Abstract

The estimation of population variance for sensitive study variables poses significant challenges due to respondents’ reluctance to provide truthful answers. In this study, we develop generalized exponential estimators for estimating the population variance of a sensitive variable by incorporating one and two auxiliary variables within the framework of randomized response models. Using Taylor series linearization and exponential series expansion, we derive the approximate bias and mean square error (MSE) expressions of the proposed estimators. These analytical results allow us to establish optimal conditions under which the new estimators outperform traditional variance estimators available in the literature. The theoretical comparison is supported by inequalities showing the superiority of the proposed methods when certain correlations and design parameters are satisfied. To further validate the performance of our estimators, we conduct a comprehensive simulation study under multiple population structures and varying levels of sensitivity. Additionally, a real data application is presented to demonstrate the practical utility and robustness of the estimators in real-world survey settings. Results from both simulation and empirical analyses confirm that the generalized exponential estimators consistently achieve lower MSE and improved efficiency compared to existing competing models. Overall, this study contributes to the advancement of variance estimation in sensitive surveys by integrating auxiliary information within RRT frameworks and by proposing more efficient generalized exponential estimators for population variance