An Improved Estimation Procedure for Estimating the Proportion of a Population Possessing Sensitive Attribute in Unrelated Question Randomized Response Technique

摘要

This paper considers the problem of estimating πA, the pro-portion of human population possessing the sensitive attribute A, using theunrelated question randomized response technique envisaged by Horvitz et.al. (1967) and Greenberg et. al. (1969). A family of estimators .πHof pop-ulation proportion πAis defined. The bias and mean squared error (MSE)of the proposed estimator .πHare obtained. "Optimum estimator" in thefamily of estimators .πHis investigated. It has been shown that the "opti-mum estimator" is always better than usual estimator. Since the optimumestimator depends on the "optimum value" of the scalar H, which is functionof unknown population parameters, so it has little practical utility. From thepractical point of view, various estimators of πAbased on di.erent estimatedoptimum values of H have been proposed with their properties. E.cienciesof the proposed estimators have been worked out numerically