Abstract
In 1965 Warner pioneered randomized response techniques to estimate the proportion of people bearing a sensitive characteristic. He restricted applying his randomized response device to gather data on sensitive issues from respondents chosen by simple random sampling with replacement (SRSWR). It has spawned numerous ramifications. We present results for the situation where the distinct persons chosen in an SRSWR are identified but each one independently gives a randomized response by Warner’s device, repeated as many times as he/she is selected. Two new estimators are proposed for the sensitive proportion and compared against relevant competitors.
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References
Arnab R (1999) On use of distinct respondents in RR surveys. Biom J 41: 507–513
Basu D (1958) On sampling with and without replacement. Sankhya 20: 287–294
Chaudhuri A (2001) Using randomized response from a complex survey to estimate a sensitive proportion in a dichotomous finite population. J Stat Plan Inf 94: 37–42
Chaudhuri A, Pal S (2008) Estimating sensitive proportions from Warner’s randomized responses in alternative ways restricting to only distinct units sampled. Metrika 68: 147–156
Christofides TC (2003) A generalized randomized response technique. Metrika 57: 195–200
Christofides TC (2005) Randomized response in stratified sampling. J Stat Plan Inf 128: 303–310
Horvitz DG, Thompson DJ (1952) A generalization of sampling without replacement from a finite universe. J Am Stat Assoc 47: 663–685
Korwar RM, Serfling RJ (1970) On averaging over distinct units in sampling with replacement. Ann Math Stat 41: 2132–2134
Mangat NS (1994) An improved randomized response strategy. J R Stat Soc Ser B (Methodological) 56(1): 93–95
Mangat NS, Singh R (1990) An alternative randomized response procedure. Biometrika 77: 439–442
Mangat NS, Singh R, Singh S, Bellhouse DR, Kashani HB (1995) On efficiency of estimator using distinct respondents in randomized response survey. Surv Methodol 21: 21–23
Pathak PK (1962) On simple random sampling with replacement. Sankhya A 24: 287–302
Raj D, Khamis SH (1958) Some remarks on sampling with replacement. Ann Math Stat 39: 550–557
Singh S, Mahmud M, Tracy DS (2001) Estimation of mean and variance of stigmatized quantitative variable using distinct units in randomized response sampling. Stat Papers 42: 403–411
Warner SL (1965) Randomized response: a survey technique for eliminating evasive answer bias. J Am Stat Assoc 60: 63–69
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Chaudhuri, A., Bose, M. & Dihidar, K. Estimating sensitive proportions by Warner’s randomized response technique using multiple randomized responses from distinct persons sampled. Stat Papers 52, 111–124 (2011). https://doi.org/10.1007/s00362-009-0210-3
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DOI: https://doi.org/10.1007/s00362-009-0210-3