Efficient Estimation of Population Variance of a Sensitive Variable Using a New Scrambling Response Model

Abstract

Abstract In this study, a new scrambling response model is introduced to deal with a sensitive variable, and then following the proposed scrambling response model, a generalized estimator for variance estimation of sensitive variable based-on two auxiliary information. The expressions of the bias, the mean square error, and the minimum mean square error are derived up to the first order of approximation. Simulation and empirical results show that the proposed generalized estimator under both scrambling response models attains minimum mean square error as compared to existing estimators. Also, the degree of privacy protection of the respondent for the proposed model is evaluated through simulation and empirical study.