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

Abstract

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.

Keywords:

• Protection and efficiency
• Sensitive characteristic
• Two-deck randomized response model
• Unrelated characteristic

MATHEMATICS SUBJECT CLASSIFICATION:

• 62D05

Acknowledgments

The authors are thankful to the Editor-in-Chief Prof. Narayanaswamy Balakrishnan, Admin. Debbie Iscoe, and Priyanka Udaykumar, and two referees for their valuable comments on the original version of this manuscript.