Estimation of Sensitive Study Variable Using Randomized Response Model Under Systematic Sampling

This study addresses the important problem of estimating sensitive study variables when respondents may be reluctant to provide truthful answers due to privacy concerns. In such situations, scrambled response techniques are widely used because they protect the respondent’s confidentiality while still allowing reliable estimation of population characteristics. In this paper, we propose a generalized exponential estimator for estimating the population mean of a sensitive study variable using systematic sampling. A distinguishing feature of this research is the incorporation of the randomized response technique (RRT) into the systematic sampling framework, together with the inclusion of the logarithmic function in the proposed estimator, to improve the estimation of sensitive characteristics while making effective use of auxiliary information. The expressions for the approximate bias and mean square error (MSE) of the proposed estimator are derived using the Taylor and exponential series expansions. An efficient class of exponential-type estimators is obtained by employing different choices of robust parameters of the auxiliary variable. Theoretical comparisons of the proposed estimator are made with the sample mean, modified ratio, and modified exponential ratio estimators. A simulation study is conducted to evaluate the performance of the proposed estimator using five simulated populations at different levels of correlation. The theoretical results, simulation study and real data application show that the proposed estimator provides lower MSE and higher efficiency than the competing estimators under a wide range of conditions.