A two-stage design for multivariate estimation of proportions

ABSTRACT

In this article, the problem of estimation of the several proportions of two inter-dependent sensitive characteristics prevailing in a given population is considered. A new two-stage randomized response model has been proposed by extending Lee et al.’s (2013 Lee, C., Sedory, S., Singh, S (2013). Estimation at least seven measures of qualitative variables from a single sample using randomized response technique. Stat. Probab. Lett. 83(1):399–409.[Crossref], [Web of Science ®] , [Google Scholar]) model. The expressions for biases, variances, and mean square errors of different estimators have been provided. The relative efficiency comparisons of the proposed estimators has been made, numerically by considering the different practicable choices of the design parameters. It was observed that the proposed extended version performs efficiently than simple and crossed models of Lee et al. (2013 Lee, C., Sedory, S., Singh, S (2013). Estimation at least seven measures of qualitative variables from a single sample using randomized response technique. Stat. Probab. Lett. 83(1):399–409.[Crossref], [Web of Science ®] , [Google Scholar]).