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In this paper, we lower the Cramer-Rao Lower bound of variance due to Singh and Sedory ( 2011 ,  2012 ) for the Odumade and Singh ( 2009 ) model in the sense that we propose a randomized response model that is more efficient. We investigate the properties of the proposed model under various situations for protection and efficiency. The adjustment makes use of known proportion of unrelated characteristics. The situation where the proportions of the unrelated characteristics are unknown is also discussed. In addition, we wrote SAS codes to simulate various data sets in order to compute the simulated relative efficiency values.

Lowering the Cramer-Rao lower bounds of variance in randomized response sampling