Alternative estimation procedures for estimating the population proportion using Mahmood et al. (1998) Technique-I

In this paper, we have considered the problem of estimation of π_A, the proportion of human population possessing the sensitive attribute A, using the Mahmood et al. (1998) randomized response Technique-I. The suggested class allows for the improvement in efficiency due to the proposed recommendation. A family of estimators π̂M_{1 λ} of population proportion π_A is defined. Bias and mean squared error of the proposed family of estimators are obtained for performance evaluation. A family of optimum estimators is also defined. Since the optimum estimator depends on the unknown value of the constant λ, it needs to be estimated. So from the practical point of view, various estimators of π_A based on different estimated optimum values of λ have been proposed with their properties. Efficiencies of all the considered estimators are worked out numerically which indicate that proposal of the study is quite effective to enhance the performance of proportion estimator.