A new stratified three-stage unrelated randomized response model for estimating a rare sensitive attribute based on the Poisson distribution

ABSTRACT

This article suggests an efficient method of estimating a rare sensitive attribute which is assumed following Poisson distribution by using three-stage unrelated randomized response model instead of the Land et al. model (2011) when the population consists of some different sized clusters and clusters selected by probability proportional to size(:pps) sampling. A rare sensitive parameter is estimated by using pps sampling and equal probability two-stage sampling when the parameter of a rare unrelated attribute is assumed to be known and unknown.

We extend this method to the case of stratified population by applying stratified pps sampling and stratified equal probability two-stage sampling. An empirical study is carried out to show the efficiency of the two proposed methods when the parameter of a rare unrelated attribute is assumed to be known and unknown.

KEYWORDS:

• Poisson distribution
• probability proportional to size sampling
• rare sensitive attribute
• rare unrelated attribute
• stratified sampling
• two-stage unrelated question model.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62D05

Acknowledgement

The authors are thankful to the editor-in-chief, Professor N. Balakrishnan, and to the anonymous learned referees for their valuable suggestions regarding improvement of the paper.

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT and future Planning(2015R1A2A2A 01003699).

Additional information

Funding

National Research Foundation [2015R1A2A2A 01003699].