A design-based randomized response procedure for the estimation of population proportion and sensitivity level. (English) Zbl 1182.62014
Summary: A general design-based approach to randomized response surveys is proposed. The method is tailored for the joint estimation of the proportion of individuals in the population bearing a sensitive attribute and the proportion of individuals in the sensitive group declaring truthfully their status. The proposal is specialized to the case of simple random sampling without replacement, unequal probability sampling without replacement and stratified sampling.
MSC:
| 62D05 | Sampling theory, sample surveys |
Keywords:
randomized response procedure; design-based approach; proportion estimation; sensitivity level estimationReferences:
| [1] | Arnab, R., Randomized response trials: a unified approach for qualitative data, Comm. Statist. Theory Methods, 25, 1173-1183 (1996) · Zbl 0875.62052 |
| [2] | Barabesi, L.; Marcheselli, M., A practical implementation and Bayesian estimation in Franklin’s randomized response procedure, Comm. Statist. Simulation Comput., 35, 563-573 (2006) · Zbl 1093.62014 |
| [3] | Bellhouse, D. R., Linear model for randomized response designs, J. Amer. Statist. Assoc., 75, 1001-1004 (1980) · Zbl 0456.62012 |
| [4] | Brewer, K. R.W.; Hanif, M., Sampling with Unequal Probabilities (1983), Springer: Springer New York · Zbl 0514.62015 |
| [5] | Chang, H. J.; Huang, K. C., Estimation of proportion and sensitivity of a qualitative character, Metrika, 53, 269-280 (2001) · Zbl 1008.62519 |
| [6] | Chang, H. J.; Liang, D. H., A two-stage unrelated randomized response procedure, Austral. J. Statist., 38, 43-51 (1996) · Zbl 0888.62006 |
| [7] | Chaudhuri, A., Randomized response surveys of finite populations: a unified approach with quantitative data, J. Statist. Plann. Inference, 15, 157-165 (1987) · Zbl 0615.62009 |
| [8] | Chaudhuri, A., Using randomized response from a complex survey to estimate a sensitive proportion in dichotomous finite population, J. Statist. Plann. Inference, 94, 37-42 (2001) · Zbl 0971.62002 |
| [9] | Chaudhuri, A.; Mukerjee, R., Randomized Response: Theory and Techniques (1988), Marcel Dekker: Marcel Dekker New York · Zbl 0643.62002 |
| [10] | Chaudhuri, A.; Saha, A., Optimal versus compulsory randomized response techniques in complex surveys, J. Statist. Plann. Inference, 135, 516-527 (2005) · Zbl 1162.62302 |
| [11] | Chaudhuri, A.; Stenger, H., Survey Sampling: Theory and Methods (1992), Marcel Dekker: Marcel Dekker New York · Zbl 0779.62008 |
| [12] | Christofides, T. C., Randomized response in stratified sampling, J. Statist. Plann. Inference, 128, 303-310 (2005) · Zbl 1095.62011 |
| [13] | Eriksson, S., A new model for randomized response, Internat. Statist. Rev., 41, 101-113 (1973) · Zbl 0287.92008 |
| [14] | Franklin, L. A., A comparison of estimators for randomized response sampling with continuous distributions from a dichotomous population, Comm. Statist. Theory Methods, 18, 489-505 (1989) · Zbl 0696.62014 |
| [15] | Godambe, V. P., Estimation in randomized response trials, Internat. Statist. Rev., 48, 29-32 (1980) · Zbl 0451.62011 |
| [16] | Hedayat, A. S.; Sinha, B. K., Design and Inference in Finite Population Sampling (1991), Wiley: Wiley New York · Zbl 0850.62160 |
| [17] | Horvitz, D.G., Shah, B.V., Simmons, W.R., 1967. The unrelated question randomized response model. In: Proceedings of the ASA Social Statistics Section, pp. 65-72.; Horvitz, D.G., Shah, B.V., Simmons, W.R., 1967. The unrelated question randomized response model. In: Proceedings of the ASA Social Statistics Section, pp. 65-72. |
| [18] | Huang, K. C., A survey technique for estimating the proportion and sensitivity in a dichotomous finite population, Statist. Neerlandica, 58, 75-82 (2004) · Zbl 1090.62512 |
| [19] | Kim, J. M.; Warde, W. D., A stratified Warner’s randomized response model, J. Statist. Plann. Inference, 120, 155-165 (2004) · Zbl 1232.62033 |
| [20] | Kuk, A. Y.C., Asking sensitive questions indirectly, Biometrika, 77, 436-438 (1990) · Zbl 0711.62011 |
| [21] | Mangat, N. S.; Singh, R., An alternative randomized response procedure, Biometrika, 77, 439-442 (1990) · Zbl 0713.62011 |
| [22] | Marcheselli, M.; Barabesi, L., A generalization of Huang’s randomized response procedure for the estimation of population proportion and sensitivity level, Metron, LXIV, 145-159 (2006) · Zbl 1416.62086 |
| [23] | Saha, A., Optional randomized response in stratified unequal probability sampling. A simulation based numerical study with Kuk’s method, Test, 16, 346-354 (2007) · Zbl 1119.62010 |
| [24] | Särndal, C. E.; Swensson, B.; Wretman, J., Model Assisted Survey Sampling (1992), Springer: Springer New York · Zbl 0742.62008 |
| [25] | Singh, R.; Mangat, N. S., Elements of Survey Sampling (1996), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0937.62546 |
| [26] | Singh, S., Advanced Sampling Theory with Applications (2003), Kluwer Academic Publisher: Kluwer Academic Publisher Dordrecht · Zbl 1145.62304 |
| [27] | Warner, S. L., Randomized response: a survey technique for eliminating evasive answer bias, J. Amer. Statist. Assoc., 60, 63-69 (1965) · Zbl 1298.62024 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
