An alternative to Odumade and Singh’s generalized forced quantitative randomized response model: A unified approach

Abstract

This paper considers the problem of estimating the population total of the sensitive variable under a unified approach. Odumade and Singh (2008) have suggested a forced quantitative randomized response model and then suggested an unbiased estimator of the population total $Y$ of the sensitive variable $y$ . It is observed that the optimum estimator of the population total $Y$ due to Odumade and Singh (2008) depends on the unknown population parameter under investigation which lacks the practical utility. To overcome this drawback Odumade and Singh (2008) suggested another unbiased estimator of the population total of the sensitive variable based on two independent samples which causes the increase in the cost. Keeping this in view we define an alternative randomized response procedure and hence the estimator of the population total of the sensitive variable based on one sample only which is free from such limitation and more efficient than the Odumade and Singh (2008) estimator. The relative efficiency of the proposed estimator with respect to Bar-Lev et al. (2004) and Odumade and Singh (2008) estimators are examined through numerical illustration.