A Novel Forced Scrambling Model Under Time-Scaled Surveys for Estimation of Population Variance

Abstract

In survey sampling, forced randomized response models are special variants of traditional models employed by researchers in sensitive surveys. The existing forced models are based on traditional one-time surveys where the respondents are interviewed only at a single time-point. These existing one-time survey-based models suffer from a serious drawback - the scrambling process is performed only once by each respondent. The lack of replication usually results in measurement errors which often have a negative influence on the estimators of population parameters. This study reveals that time-scaled surveys provide more efficient estimates of the population variance of sensitive variables than the traditional one-time surveys, under forced randomized response models. An Exponentially Weighted Moving Average (EWMA) estimator is used to estimate the population variance, based on the responses obtained at different time points. Further, a new forced randomized scrambling model is also proposed and the improvement over the available models is observed.