A simple way of improving the Bar–Lev, Bobovitch and Boukai Randomized response model
Keywords:
Estimation of proportion, randomized response sampling, respondents protection, sensitive quantitative variable.Abstract
Eichhorn & Hayre (1983) considered a randomized response procedure suitable for estimating the mean response, when the sensitive variable under investigation is quantitative in nature. They have obtained an estimate for the mean of the quantitative response variable under investigation and studied its properties. Bar–Lev et al. (2004) have suggested an alternative procedure, which use a design parameter (controlled by the experimenter) that generalizes Eichhorn & Hayre’s (1983) results. They have also proved that the estimator proposed by them has uniformly smaller variance as compared to that of Eichhorn & Hayre (1983) in certain condition. In this paper we have suggested a simple procedure of improving the Eichhorn & Hayre (1983) and Bar–Lev et al. (2004) models along with its properties. It has been shown that the proposed procedure is uniformly better than Bar–Lev et al. (2004) procedure. The proposed procedure is also uniformly better than Eichhorn and Hayre’s (1983) procedure under the same condition in which the Bar–Lev et al.’s (2004) procedure is more efficient than Eichhorn & Hayre’s (1983) procedure. Numerical illustration is given in support of the present study.
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