Use of weights in mixed randomized response model

Abstract

In this paper, we have suggested a weighted unbiased estimator based on mixed randomized response model. Some unbiased estimators are generated from the proposed weighted estimator. The variance of the proposed weighted estimator is obtained and relevant condition is obtained in which the proposed weighted estimator is superior to Singh and Tarray (Sociol Methods Res 44(4):706–722, 2014) estimator. It is interesting to mention that we have investigated an estimator $\hat{\pi }_{{{\text{HS}}\left( 1 \right)}}$ which is the member of the suggested weighted estimator $\hat{\pi }_{\text{HS}}$ provide better efficiency than the Singh and Tarray’s (2014) estimator $\hat{\pi }_{\text{h}}$ and close to the optimum estimator $\hat{\pi }_{\text{HS}}^{{\left( {\text{o}} \right)}}$. Thus, the estimator $\hat{\pi }_{{{\text{HS}}\left( 1 \right)}}$ is an alternative to optimum estimator $\hat{\pi }_{\text{HS}}^{{\left( {\text{o}} \right)}}$. The study is further extended in case of stratified random sampling.