Efficient estimation of the population variance using a novel optional scrambling model

In the past few years, survey researchers have developed variance estimators of sensitive variables under randomized response techniques. \textcolor{black}{ The available variance estimators utilize linear scrambling models in which all of the survey participants are forced to scramble their responses and thus hide their true responses. In practice, some of the respondents may have no problem in reporting their true response to the researcher. The current study finds that using a true response option produces more efficient estimates of population variance compared to a linear scrambling model.} Additionally, we also suggest a new variance estimator of a sensitive variable of interest and analyze its algebraic properties using an auxiliary variable. We also conduct a simulation study to show the improvement over the existing estimators of the population variance.