Analyzing Measurement Error in Sensitive Mean Estimation: A Two-Occasion Successive Sampling Approach

Abstract This study investigates the estimation of a sensitive population mean within a two-occasion successive sampling framework by employing calibration estimators in the presence of measurement error. Several calibration-based estimators are proposed by integrating Compulsory and Optional Randomized Response Techniques at both sampling occasions while explicitly accounting for measurement error. The efficiency of the proposed estimators is examined and compared with their corresponding direct estimators in order to assess the impact of measurement error on estimation accuracy. To illustrate the practical applicability of the suggested methodology, a simulation study based on a natural population associated with COVID-19 infection is conducted, demonstrating the implementation of Compulsory and Optional Randomized Response Techniques across both sampling occasions.