This article addresses the problem of estimating the proportion π S of the population belonging to a sensitive group using optional randomized response technique in stratified sampling based on Mangat model that has proportional and Neyman allocation and larger gain in efficiency. Numerically, it is found that the suggested model is more efficient than Kim and Warde stratified randomized response model and Mangat model.
In sample surveys, it is usual to increase the efficiency of the estimators by the use of the auxiliary information. We propose a class of ratio estimators of a finite population mean using two auxiliary variables and obtain mean square error (MSE) equations for the class of proposed estimators. We find theoretical conditions that make proposed family estimators more efficient than the traditional ratio estimator and the estimators proposed by Abu-Dayeh et al. using two auxiliary variables. In addition, we support these theoretical results with the aid of a numerical example.
There have been many alternative strategies for implementing sampling survey on quantitative characteristic of sensitive issues by using randomized response (RR) technique. The efficiency of most of those strategies has been improved by choosing the suitable design parameters of model. However, the two different procedures with pre-assigned design parameter values cannot ensure that they possess the same protection degree to the respondents. Some earlier comparisons of those strategies are inadequate (as in Eichhorn and Hayre, 1983;Gupta et al., 2002). Some literature contains a more comprehensive comparison based on efficiency and protection degree to the respondents among the qualitative characteristic RR techniques (see Bhargava and Singh, 2002;Nayak, 1994;Zaizai and Zankan, 2004). As far as the comparisons are concerned that are based on efficiency and protection degree to the respondents among the quantitative characteristic RR techniques, very few related studies have been found so far. The purpose of this article is to give a more adequate comparison among those earlier quantitative characteristic RR strategies. It is found that several important differences between the results obtained in this article and some known results exist. Therefore, these earlier RR strategies should be reevaluated.
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