An Improved Quantitative Optional Randomised Response Technique with Additive Scrambling using Two Questions Approach

Yıl 2024, Cilt: 7 Sayı: 2, 104 - 113, 30.06.2024

Neeraj Tiwari Tanuj Kumar Pandey

https://doi.org/10.33434/cams.1435108

Öz

In this paper, an improved two-stage and three-stage optional randomized response (ORR) models for quantitative variables that make the use of additive scrambling was proposed. These two-stage and three-stage models achieve efficient estimation of the mean and sensitivity level simultaneously in the single sample by using two questions. It is found that the proposed models perform better than the existing ORR models in terms of estimating sensitive attribute and sensitivity level simultaneously. It is found that the proposed three stage ORR model provides better estimates than the two-stage and one-stage ORR models and offers more privacy to the respondents with suitable choice of design parameters. The properties of the proposed models are demonstrated with the help of a numerical study.

Anahtar Kelimeler

Optional randomised response, Sensitive surveys, Sensitivity level, Two-questions approach

Kaynakça

• [1] S. L. Warner, Randomized response: a survey technique for eliminating evasive answer bias, J. Amer. Stat. Assoc., 60(309) (1965), 63–69.
• [2] S. L. Warner, Linear randomized response models, J. Amer. Stat. Assoc., 66 (1971), 884–888.
• [3] K. H. Pollock, Y. Bek, A comparison of three randomized response models for quantitative data, J. Amer. Stat. Assoc., 71(356) (1976), 884-886.
• [4] B. G. Greenberg, R. R. Kuebler, J. R. Abernathy, D. G. Horvitz, Application of the randomized response technique in obtaining quantitative data, J. Amer. Statist. Assoc., 66(334) (1971), 243-250.
• [5] B. H. Eichhorn, L. S. Hayre, Scrambled randomized response methods for obtaining sensitive quantitative data, J. Stat. Plan. Infer., 7(4) (1983), 307-316.
• [6] S. Gupta, B. Gupta, S. Singh, Estimation of sensitivity level of personal interview survey questions, J. Stat. Plan. Infer., 100(2) (2002), 239-247.
• [7] S. N. Gupta, B. Thornton, J. Shabbir, S. Singhal, A comparison of multiplicative and additive optional RRT models, J. Stat. Theo. Appl., 5 (2006), 226–239.
• [8] S. Gupta, J. Shabbir, S. Sehra, Mean and sensitivity estimation in optional randomized response models, J. Stat. Plan. Infer. 140 (2010), 2870-2874.
• [9] S. Mehta, B. K. Dass, J. Shabbir, S. N. Gupta, A three-stage optional randomised response model, J. Stat. Theo. Pract., 6 (2012), 417-427.
• [10] K. C. Huang, Unbiased estimators of mean, variance and sensitivity level for quantitative characteristics in finite population sampling, Metrika, 71 (2010), 341-352.
• [11] S. N. Gupta, S. Mehta, J. Shabbir, B. Dass, Generalized scrambling in quantitative optional randomized response models, Comm. Stat.: Theo. Meth., 42(22) (2013), 4034-4042.
• [12] S. Gupta, G. Kalucha, J. Shabbir, B. K. Dass, Estimation of finite population mean using optional RRT models in the presence of nonsensitive auxiliary information, Amer. J. Math. Manag. Sci., 33(2) (2014), 147–159.
• [13] N. Tiwari, P. Mehta, An improved two stage optional RRT model, J. Ind. Soc. Agr. Stat., 70(3) (2016), 197-203.
• [14] N. Tiwari, P. Mehta, Additive randomized response model with known sensitivity level, Int. J. Comp. Theor. Stat. 4(2) (2017).
• [15] G. Narjis, J. Shabbir, Estimation of population proportion and sensitivity level using optional unrelated question randomized response techniques, Comm. Stat. Sim. Comp., 49(12) (2020), 3212-3226.
• [16] J. S. Sihm, A. Chhabra, S. N. Gupta, An optional unrelated question RRT model, Involve J. Math., 9(2) (2016), 195-209.
• [17] A. Chhabra, B. K. Dass, S. Mehta, Multi-stage optional unrelated question RRT model, J. Stat. Theo. Appl., 15(1) (2016), 80-95.
• [18] G. Kalucha, S. N. Gupta, J. Shabbir, A two-step approach to ratio and regression estimation of finite population mean using optional randomized response models, Hac. J. Math. Stat., 45(6) (2016), 1819–1830.
• [19] G. Narjis, J. Shabbir, Estimating the prevalence of sensitive attribute with optional unrelated question randomized response models under simple and stratified random sampling, Sci. Iran., 28(5) (2021), 2851-2867.
• [20] S. Gupta, J. Zhang, S. Khalil, P. Sapra, Mitigating lack of trust in quantitative randomized response technique models, Commun. Stat. Sim. Comp., (2022), 1-9.
• [21] G. Diana, P. F. Perri, A class of estimators for quantitative sensitive data, Stat. Papers, 52 (2011), 633-650.
• [22] M. Azeem, I. M. Asadullah, S. Hussain, N. Salahuddin, A. Salam, A novel randomized scrambling technique for mean estimation of a finite population, Hel., 10(11), e31690.
• [23] J. A. Fox, P. E. Tracy, Quantitative Applications In The Social Sciences: Randomized Response, Newbury Park, CA: SAGE Publications, Inc., 1986.
• [24] A. Chaudhuri, T. C. Christofides, C. R. Rao, Handbook of Statistics, Volume 34, Data Gathering, Analysis and Protection of Privacy Through Randomized Response Techniques: Qualitative and Quantitative Human Traits, North-Holland. 2016.
• [25] T. N. Le, S. M. Lee, P. L. Tran, C. S. Li, Randomised response techniques: A systematic review from the pioneering work of Warner (1965) to the present, Mathematics, (2023), 1718.
• [26] B. G. Greenberg, A. L. A. Abul-Ela, W. R. Simmons, D. G. Horvitz, The unrelated question randomized response model: Theoretical framework, J. Amer. Statist. Assoc., 64(326) (1969), 520-539.
• [27] J. Lanke, On the degree of protection in randomized interviews, Int. Stat. Rev., 44(2), (2016), 197-203.
• [28] Z. Yan, J.Wang, J. Lai, An efficiency and protection degree-based comparison among the quantitative randomized response strategies, Comm. Stat. Theo. Meth., 38 (2009), 400-408.
• [29] S. Giordano, P. F. Perri, Efficiency comparison of unrelated question models based on same privacy protection degree, Stat. Papers, 53 (2012), 987-999.
• [30] Z. Hussain, M. M. Al-Sobhi, B. Al-Zahrani, H. P. Singh, T. A. Tarray, Improved randomized response approaches for additive scrambling models, Math. Pop. Stud., 23(4) (2016), 205–221.