Advertisement

Journal of Statistical Theory and Practice

, Volume 6, Issue 2, pp 376–381 | Cite as

Unbiased Estimation of a Sensitive Proportion in General Sampling by Three Nonrandomized

  • Arijit Chaudhuri
Article
  • 2 Downloads

Abstract

Contrasting with well-publicized randomized response (RR) techniques (RRT) claimed to be useful in estimating the proportion of people bearing a sensitive characteristic in a given community, recently nonrandomized response (NRR) techniques (NRRT) are emerging. As with most early RRTs, the NRRTs to date are applied exclusively to samples selected by simple random sampling (SRS) with replacement (SRSWR) scheme alone. This article shows how three NRR schemes in vogue may be used in unbi-ased estimation even when a sample may be selected following a general scheme. The current literature stresses maximum likelihood estimation (MLE) rather than unbiased estimation (UE) when these NRR schemes are employed.

AMS Subject Classification

62D05 

Key-words

Alternatives to RR in data gathering on sensitive items Estimating a proportion bearing a stigmatizing feature General sampling designs 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chaudhuri, A. 2001. Using randomized response from a complex survey to estimate a sensitive proportion in a dichotomous finite population. J. Stat. Plan. Inf., 92, 37–42MathSciNetCrossRefGoogle Scholar
  2. Chaudhuri, A. 2010. Essentials of survey sampling. New Delhi, India, Prentice Hall of India.Google Scholar
  3. Chaudhuri, A. 2011. Randomized response and indirect questioning techniques in surveys. Boca Raton, FL, Chapman and Hall, CRC Press, Taylor and Francis.zbMATHGoogle Scholar
  4. Chaudhuri, A., and Pal, S. 2002. Estimating proportions from unequal probability samples using randomized responses by Warner’s and other devices. J. Ind. Soc. Agric. Stat. 55(2), 174–183.MathSciNetzbMATHGoogle Scholar
  5. Christofides, T. C. 2009. Randomized response without a randomization device. Adv. Appl. Stat., 11, 15–28.MathSciNetzbMATHGoogle Scholar
  6. Horvitz, D. G, and Thompson, D. J. 1952. A generalization of sampling without replacement from a finite universe. J. Am. Stat. Assoc., 47, 653–684.MathSciNetCrossRefGoogle Scholar
  7. Pal, S. 2007. Extending Takahasi-Sakasegawa’s indirect response techniques to cover sensitive surveys in unequal probability sampling. Cal. Stat. Assoc. Bull. 59, 265–276.MathSciNetGoogle Scholar
  8. Sousa, R., J. Shabbir, P. C. Real, and S. Gupta. 2010. Ratio estimation of the mean of a sensitive variable in the presence of auxiliary information. J. Stat. Theory Pract, 4(3), 495–507.MathSciNetCrossRefGoogle Scholar
  9. Takahasi, K., and H. Sakasegawa. 1977. An RR technique without use of any randomizing device. Ann. Inst. Stat. Math., 29, 1–8.CrossRefGoogle Scholar
  10. Tan, M. T., G. L. Tian, and M. L. Tang. 2009. Sample surveys with sensitive questions: A non-randomized response approach. Am. Stat., 63(1), 1–9.CrossRefGoogle Scholar
  11. Tian, G. L., J. W. Yu, M. L. Tang, and Z. Geng. 2007. A new non-randomized model for analyzing sensitive questions with binary outcomes. Stat. Med., 26(23), 4238–4252.MathSciNetCrossRefGoogle Scholar
  12. Warner, S. L. 1965. RR: A survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc., 60, 63–69.CrossRefGoogle Scholar
  13. Yates, F. and P. M. Grundy. 1953. Selection without replacement from within strata with probability proportional to size. J. R. Stat. Soc. Ser. B, 15, 253–261.zbMATHGoogle 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 2011

Authors and Affiliations

  1. 1.Indian Statistical InstituteKolkataIndia

Personalised recommendations