Optimal strategy for improved estimation of population mean of sensitive variable using non-sensitive auxiliary variable

To improve the transformed ratio type estimators, this study uses new population parameters that are derived from extra information using a randomized response technique (RRT). Additionally, we suggest a modified family of powerful estimators for estimating the population mean of the sensitive variable in the presence of auxiliary data that are not sensitive. The bias and mean squared error (MSE), which are the primary statistical characteristics of the proposed estimator, have been determined up to the first order of approximation. We conduct theoretical comparisons among the contending estimators. Theoretical claims are supported by empirical evidence obtained from actual datasets. The suggested and competing estimators are further compared by analyzing their performances on a simulated data set. For a wide range of sensitive research applications, it is advisable to choose an estimator that possesses desirable sample properties and a minimized mean squared error (MSE). © The Author(s) 2025.