Efficient Bayes estimators of sensitive proportion with simple and mixture priors using direct and indirect responses

In this study, efficient Bayes estimators of sensitive proportion are proposed. It is documented that indirect reports increase variances of the estimates. To counteract this increase in variances we divided the total sample size, n = n(1)+n(2), such that n(1) individuals record direct responses and n(2) individuals record indirect responses. The decision that a group of individuals should report indirect or direct responses would be based on distinct known factors. Bayes estimates and subsequent posterior risks are calculated taking into account different prior distributions, loss functions and a generalized randomized response technique. The impact of design parameters and the number of responses obtained using direct and indirect questioning techniques on the relative efficiencies are investigated. Graphical and numerical results indicate that the proposed estimators are better than the existing.