A New Optimal Estimator of Population Proportion in Randomized Response Sampling

A new optimal estimator of population proportion of potentially sensitive attributes in survey sampling is proposed and investigated. The proposed estimator makes use of known average values and known common variance of two scrambling variables at the data collection and estimation stages; more cooperation is expected from the respondents than in the Franklin (1989) model. The variance of the proposed estimator is minimized to determine the value of a constant which leads to an optimal estimator of the population proportion. The resulting optimal estimator has been found to be more efficient than the Franklin (1989) estimator, and the Singh and Chen (2009) estimator which suggest utilizing higher order moments of scrambling variables at the estimation stage.