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Journal of Statistical Theory and Practice

, Volume 8, Issue 2, pp 319–342 | Cite as

Applying the Nonrandomized Diagonal Model to Estimate a Sensitive Distribution in Complex Sample Surveys

Article

Abstract

In surveys with a sensitive characteristic X, such as income or tax evasion, direct questioning causes answer refusal and untruthful answers. To increase the respondents’ cooperation, nonrandomized response survey techniques are currently emerging. In this field of research, the diagonal model (DM) survey technique was recently published to gather data on multicategorical X. However, the estimation of the distribution of X from DM data is so far only derived for simple random sampling with replacement. To overcome this limitation, we develop in this article DM estimates for complex sampling designs that are often applied in practice, including stratified, cluster, multistage, and unequal probability sampling. Here, we apply quadratic programming to obtain admissible estimates in the unit simplex for the probability masses of X. Bootstrap variance estimates for the admissible estimators are described, and a method to investigate the connection between estimation efficiency in complex sample surveys and the degree of privacy protection by simulations is established. Our simulations show that larger efficiency corresponds to lower privacy protection and indicate optimal parameters for the DM. Such optimality results are rare in the existing literature on privacy-protecting survey models for multicategorical sensitive variables, especially for complex sampling designs.

Keywords

Untruthful answers Answer refusal Randomized response Inadmissible estimates for multinomial proportions in complex sampling Bootstrap variance estimates Degree of privacy protection 

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References

  1. Barbiero, A., and F. Mecatti. 2010. Bootstrap algorithms for variance estimation in π PS sampling. In Complex data modeling and computationally intensive statistical methods, ed. P. Mantovan and P. Secchi, 57–69. Milan, Italy: Springer.CrossRefGoogle Scholar
  2. Chao, M. T., and S. H. Lo. 1985. A bootstrap method for finite populations. Sankhya Ser. A, 47, 399–405.MathSciNetMATHGoogle Scholar
  3. Chaudhuri, A. 2011. Randomized response and indirect questioning techniques in surveys. Boca Raton, FL: Chapman & Hall/CRC.MATHGoogle Scholar
  4. Chaudhuri, A. 2012. Unbiased estimation of a sensitive proportion in general sampling by three nonrandomized response schemes. J. Stat. Theory Pract., 6, 376–381.MathSciNetCrossRefGoogle Scholar
  5. Efron, B. 1979. Bootstrap methods: Another look at the jackknife. Ann. Stat., 7, 1–26.MathSciNetCrossRefGoogle Scholar
  6. Groenitz, H. 2012. A new privacy-protecting survey design for multichotomous sensitive variables. Metrika. doi:10.1007/s00184-012-0406-8.CrossRefMathSciNetMATHGoogle Scholar
  7. Rao, J. N. K., and C. F. J. Wu. 1988. Resampling inference with complex survey data. J. Am. Stat. Asso., 83, 231–241.MathSciNetCrossRefGoogle Scholar
  8. Särndal, C. E., B. Swensson, and J. Wretman. 1992. Model assisted survey sampling. New York, NY: Springer.CrossRefGoogle Scholar
  9. Shao, J., and D. Tu. 1995. The jackknife and bootstrap. New York, NY: Springer.CrossRefGoogle Scholar
  10. Sitter, R. R. 1992. Comparing three bootstrap methods for survey data. Can. J. Stat., 20, 135–154.MathSciNetCrossRefGoogle Scholar
  11. Tan, M. T., G. L. Tian, and M. L. Tang. 2009. Sample surveys with sensitive questions: A nonrandomized response approach. Am. Stat., 63, 9–16.MathSciNetCrossRefGoogle Scholar
  12. Tang, M. L., G. L. Tian, N. S. Tang, and Z. Liu. 2009. A new non-randomized multi-category response model for surveys with a single sensitive question: Design and analysis. J. Korean Stat. Soc., 38, 339–349.MathSciNetCrossRefGoogle Scholar
  13. Tian, G. L., J. W. Yu, M. L. Tang, and Z. Geng. 2007. A new non-randomized model for analysing sensitive questions with binary outcomes. Stat. Med., 26, 4238–4252.MathSciNetCrossRefGoogle Scholar
  14. Yu, J. W., G. L. Tian, and M. L. Tang. 2008. Two new models for survey sampling with sensitive characteristic: design and analysis. Metrika, 67, 251–263.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2014

Authors and Affiliations

  1. 1.Department of Statistics (Faculty 02)Philipps-University MarburgMarburgGermany

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