An Efficient Horvitz–Thompson-Type Estimator for Two Sensitive Means Using a Three-Stage Quantitative Randomized Response Under Complex Sampling

In many empirical studies, researchers face challenges when addressing sensitive topics as respondents may be reluctant to provide truthful answers due to privacy concerns. Traditional direct survey methods often yield biased or unreliable estimates in such contexts. The randomized response technique offers a robust alternative by improving data validity while protecting respondent confidentiality. This paper proposes a novel quantitative three-stage randomized response model, introducing a new Horvitz–Thompson (HT)-type estimator for estimating the means of two sensitive variables under a general sampling design. Simulation studies indicate that the proposed estimator can achieve lower bias and mean squared error (MSE) compared to other existing estimators in the literature. Additionally, an empirical investigation was conducted using data from Shahid Chamran University of Ahvaz to estimate the average rates of exam cheating and cigarette consumption among students under a simple random sampling scheme, further demonstrating the practical utility of the proposed approach.