Estimation of a rare sensitive attribute for two-stage randomized response model in probability proportional to size sampling using Poisson probability distribution

ABSTRACT

This paper addresses the estimation of the mean number of individuals in the population who possess a rare sensitive attribute using Poisson distribution for the situations of (i) clustered population and (ii) stratified population with clusters are strata units. Properties of the proposed estimation procedures have been discussed when the proportion of a rare unrelated non-sensitive attribute is assumed to be known as well as unknown. Empirical studies are carried out to support the theoretical results which showed dominance over Lee et al. [Estimation of a rare sensitive attribute in probability proportional to size measures using Poisson distribution. Statistics (Ber). 2014;48(3):685–709] estimation procedures.

KEYWORDS:

• Randomized response technique
• rare sensitive attribute
• rare unrelated non-sensitive attribute
• Poisson probability distribution
• probability proportional to size (pps) sampling

MATHEMATICS SUBJECT CLASSIFICATION:

• 62D05

Acknowledgements

Authors are thankful to Indian Institute of Technology (Indian School of Mines), Dhanbad for providing the necessary support to carry out the present research work, authors are also grateful to the honourable Reviewers, Editor and Associate Editor for their valuable suggestions which helped us in improving the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.