Towards the search for improving the randomized response models used to estimate a population proportion bearing a sensitive characteristic, a new model, based on the use of a two-stage randomized response procedure, is proposed. The condition under which the proposed estimator is more efficient than the Odumade and Singh [Comm. Statist. Theory Methods 38 (2009) 439–446] estimator has been obtained. An empirical study has also been performed to examine the relative efficiency of the proposed estimator with respect to the Odumade and Singh [Comm. Statist. Theory Methods 38 (2009) 439–446] estimator. Moreover, the proposed estimator can be easily adjusted to be more efficient than the Warner [J. Amer. Statist. Assoc. 60 (1965) 63–69], Mangat and Singh [Biometrika 77 (1990) 439–442], Mangat [J. R. Stat. Soc. Ser. B Stat. Methodol. 56 (1994) 93–95] and Odumade and Singh [Comm. Statist. Theory Methods 38 (2009) 439–446] estimators.
"Efficient use of a two-stage randomized response procedure." Braz. J. Probab. Stat. 27 (4) 608 - 617, November 2013. https://doi.org/10.1214/12-BJPS189