Dealing sensitive characters on successive occasions through a general class of estimators using scrambled response techniques
- 129 Downloads
Present article endeavours to propose a general class of estimators to estimate population mean of a sensitive character using non-sensitive auxiliary information under five different scrambled response models in two occasions successive sampling. Various well-known estimators have been modified for the estimation of sensitive population mean and hence they also become a member of proposed general class of estimators. Properties of proposed class of estimators have been derived and checked empirically while comparing the proposed class of estimators with respect to modified Jessen (Iowa Agric Exp Stn Res Bull 304:1–104, 1942) type estimator and modified Singh (Stat Transit 7(1):21–26, 2005) type estimator under five different scrambled response models. The effectiveness of different models has been discussed while comparing it with the direct questioning methods. A model for optimum total cost has also been proposed. Privacy protection has been elaborated for all considered models. Numerical illustrations including simulation studies are abundant to the theoretical results. Finally suitable recommendations are forwarded.
KeywordsSuccessive sampling Scrambled response model Sensitive character Class of estimators Population mean Bias Mean squared error Optimum replacement policy
Mathematics Subject Classification62D05
The authors wish to thank anonymous reviewer and Professor Giovanni Maria Giorgi, Editor in Chief for their careful reading and constructive suggestions which lead to improvement over an earlier version of the paper.
- 18.Horvitz, D.G., Shah, B.V., Simmons, W.R.: The unrelated question randomized response model. In: Proc. Soci. Statist. Amer. Statist. Asso., pp. 65–72 (1967)Google Scholar
- 20.Jessen, R.J.: Statistical investigation of a sample survey for obtaining farm facts. Iowa Agric. Exp. Stn. Res. Bull. 304, 1–104 (1942)Google Scholar
- 24.Naeem, N., Shabbir, J.: Use of scrambled responses on two occasions successive sampling under non-response. Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics, p. 46 (2016). http://www.hjms.hacettepe.edu.tr/uploads/32c18b80-275f-4b5a-a28d-6a5890eecac3.pdf
- 28.Priyanka, K., Mittal, R.: Effective rotation patterns for median estimation in successive sampling. Stat. Trans. 15(2), 197–220 (2014)Google Scholar
- 29.Priyanka, K., Mittal, R., Min-Kim, J.: Multivariate rotation design for population mean in sampling on successive occasions. Commun. Stat. Appl. Methods 22(5), 445–462 (2015)Google Scholar
- 36.Sukhatme, P.V., Sukhatme B.V., Sukhatme S., Ashok, C.: Sampling theory of surveys with applications. The Indian society of Agricultural Statistics, New Delhi. The lowa state college press, Ames, pp. xxix+491 (1984)Google Scholar
- 49.Yu, B., Jin, Z., Tian, J., Gao, G.: Estimation of sensitive proportion by randomized response data in successive sampling. Comput. Math. Methods Med. (2015). https://doi.org/10.1155/2015/172918