A practical implementation and Bayesian estimation in Franklin’s randomized response procedure. (English) Zbl 1093.62014
Summary: A Bayesian estimator, based on L. A. Franklin’s [Commun. Stat., Theory Methods 18, No. 2, 489–505 (1989; Zbl 0696.62014)] randomized response procedure is proposed for proportion estimation in surveys dealing with a sensitive character. The method is simple to implement and avoids the usual drawbacks of Franklin’s estimator, i.e., the occurrence of negative estimates when the population proportion is small. A simulation study is considered in order to assess the performance of the proposed estimator as well as the corresponding credible interval.
MSC:
62D05 | Sampling theory, sample surveys |
62F15 | Bayesian inference |
65C60 | Computational problems in statistics (MSC2010) |
Citations:
Zbl 0696.62014Software:
MathematicaReferences:
[1] | Barabesi L., J. Roy. Statist. Soc. 51 pp 105– (2002) |
[2] | Barabesi L., Metron. (2006) |
[3] | Chang H. J., Austral. J. Statist. 38 pp 43– (1996) · Zbl 0888.62006 · doi:10.1111/j.1467-842X.1996.tb00362.x |
[4] | Chaubey Y. P., J. Official Statist. 11 pp 379– (1995) |
[5] | Chaudhuri A., Randomized Response: Theory and Techniques (1988) |
[6] | Franklin L. A., Commun. Statist. Theor. Metho. 18 pp 489– (1989) · Zbl 0696.62014 · doi:10.1080/03610928908829913 |
[7] | Horvitz D. G., Proc. ASA Social Statist. Sec. pp 65– (1967) |
[8] | Kim J. M., J. Statist. Plann. Infer. 136 pp 1554– (2006) · Zbl 1088.62014 · doi:10.1016/j.jspi.2004.10.005 |
[9] | Kuk A. Y. C., Biometrika 77 pp 436– (1990) · Zbl 0711.62011 · doi:10.1093/biomet/77.2.436 |
[10] | McCullough B. D., Computat. Statist. 15 pp 279– (2000) · Zbl 0976.62001 · doi:10.1007/s001800050008 |
[11] | Mangat N. S., J. Roy. Statist. soc. 56 pp 93– (1994) |
[12] | Mangat N. S., Biometrika 77 pp 439– (1990) · Zbl 0713.62011 · doi:10.1093/biomet/77.2.439 |
[13] | Migon H. S., Computat. Statist. Data Anal. 24 pp 401– (1997) · Zbl 0900.62144 · doi:10.1016/S0167-9473(96)00075-8 |
[14] | O’Hagan A., J. Amer. Statist. Assoc. 82 pp 580– (1987) · Zbl 0657.62011 · doi:10.2307/2289468 |
[15] | Rose C., J. Roy. Statist. Soc. 49 pp 229– (2000) |
[16] | Ruskeepää H., Mathematica Navigator (1999) |
[17] | Singh S., Advanced Sampling Theory with Applications (2003) |
[18] | Unnikrishnan N. K., Sankhyā 61 pp 422– (1999) |
[19] | Warner S. L., J. Amer. Statist. Assoc. 60 pp 63– (1965) · doi:10.2307/2283137 |
[20] | Winkler R. L., J. Amer. Statist. Assoc. 74 pp 207– (1979) · doi:10.2307/2286752 |
[21] | Wolfram S., The Mathematica Book., 5. ed. (2003) · Zbl 0924.65002 |
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.