EWMA based mean estimation of sensitive variable using randomized response techniques under ranked set sampling for time-scaled surveys

In survey sampling, randomized response models serve as valuable extensions of traditional methodologies for collecting information on sensitive variables. However, existing randomized response models are restricted to single-time surveys, where the sensitive characteristic is observed only once. This one-time data collection structure poses a fundamental limitation: without repeated measurements, respondents may provide either entirely truthful or incorrect responses, and such inaccuracies can introduce substantial bias in the estimation of population parameters for sensitive variables. To address this issue, the present study develops a class of logarithmic estimators for the population mean of a sensitive variable employing randomized response models under the framework of rank set sampling for time-scaled surveys. Under the proposed time-scaled mechanism, we derive explicit expressions for the bias and mean squared error of the estimators. Furthermore, a comprehensive empirical and simulation study is conducted to examine the performance and comparative efficiency of the proposed estimators across various survey conditions.