Two-stage unrelated randomized response model to estimate the prevalence of a sensitive attribute. (English) Zbl 07876401
Summary: The present work proposes a new two-stage unrelated randomized response model to estimate the mean number of individuals who possess a rare sensitive attribute in a given population by using Poisson probability distribution, when the proportion of rare non-sensitive unrelated attribute is known and unknown. The properties of the proposed model are examined. The variance of the proposed randomized response model smaller than M. Land et al. [Statistics 46, No. 3, 351–360 (2012; Zbl 1241.62008)] and H. P. Singh and T. A. Tarray [Model Assist. Stat. Appl. 10, No. 2, 129–138 (2015; doi:10.3233/MAS-140316)] to estimate sensitive characteristic under study. The proposed model provides a more efficient unbiased estimator of the mean number of individuals. The procedure also introduces the measure of privacy protection of respondents and compares randomized response models in terms of efficiency and privacy protection. Empirical illustrations are presented to support the theoretical results and suitable recommendations are put forward to the survey statisticians/practitioners.
MSC:
| 62-08 | Computational methods for problems pertaining to statistics |
| 62D05 | Sampling theory, sample surveys |
| 62K15 | Factorial statistical designs |
Keywords:
Poisson probability distribution; unrelated randomized response model; sensitive attribute; estimation of proportion; privacy protectionCitations:
Zbl 1241.62008References:
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