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

ABSTRACT

This paper describes the estimating procedures of mean number of entities that possess a rare sensitive attribute using the Mangat (1992) randomized device, when the population consists of some clusters and the population is again stratified with some clusters in each stratum. Unbiased estimation procedures for the mean number of individuals have been discussed and their properties are described when the parameter of a rare unrelated attribute is assumed to be known and unknown. An empirical study is carried out to show the dominance of the proposed estimator over Lee et al. (2013) estimator.

KEYWORDS:

• Randomized response method
• rare sensitive attribute
• rare unrelated attribute
• Poisson distribution
• probability proportional to size (pps) sampling.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62D05

Funding

Authors are thankful to the Indian Institute of Technology (Indian School of Mines), Dhanbad, for providing the financial assistance and necessary infrastructure to carry out the present research work.