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.
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References
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, 37–42
Chaudhuri, A. 2010. Essentials of survey sampling. New Delhi, India, Prentice Hall of India.
Chaudhuri, A. 2011. Randomized response and indirect questioning techniques in surveys. Boca Raton, FL, Chapman and Hall, CRC Press, Taylor and Francis.
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.
Christofides, T. C. 2009. Randomized response without a randomization device. Adv. Appl. Stat., 11, 15–28.
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.
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.
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.
Takahasi, K., and H. Sakasegawa. 1977. An RR technique without use of any randomizing device. Ann. Inst. Stat. Math., 29, 1–8.
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.
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.
Warner, S. L. 1965. RR: A survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc., 60, 63–69.
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.
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.
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Chaudhuri, A. Unbiased Estimation of a Sensitive Proportion in General Sampling by Three Nonrandomized. J Stat Theory Pract 6, 376–381 (2012). https://doi.org/10.1080/15598608.2012.673904
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DOI: https://doi.org/10.1080/15598608.2012.673904