# zbMATH — the first resource for mathematics

Estimation of finite population proportion in randomized response surveys using multiple responses. (English) Zbl 1312.62016
Summary: We consider the problem of unbiased estimation of a finite population proportion related to a sensitive attribute under a randomized response model when independent responses are obtained from each sampled individual as many times as he/she is selected in the sample. We identify a minimal sufficient statistic for the problem and obtain complete classes of unbiased and linear unbiased estimators. We also prove the admissibility of two linear unbiased estimators and the non-existence of a best unbiased or a best linear unbiased estimator.

##### MSC:
 62D05 Sampling theory, sample surveys 62C15 Admissibility in statistical decision theory
Full Text:
##### References:
 [1] ARNAB, R, On use of distinct respondents in RR surveys, Biometrical Journal, 41, 507-513, (1999) · Zbl 0932.62009 [2] CASSEL, C. M., SARNDAL, C. E. and WRETMAN, J. H. (1977). Foundations of Inference in Survey Sampling. John Wiley, New York. · Zbl 0391.62007 [3] CHAUDHURI, A. (2011). Randomized Response and Indirect Questioning Techniques in Surveys. CRC Press, Chapman and Hall, Taylor & Francis Group. Boca Raton, Florida,USA. · Zbl 1278.62001 [4] CHAUDHURI, A; BOSE, M; DIHIDAR, K, Estimating sensitive proportions by warner’s randomized response technique using multiple responses from distinct persons, Statistical Papers, 52, 111-124, (2011) · Zbl 1247.62013 [5] CHAUDHURI, A; BOSE, M; DIHIDAR, K, Estimation of a sensitive proportion by warner’s randomized response data through inverse sampling, Statistical Papers, 52, 343-354, (2011) · Zbl 1247.62014 [6] CHAUDHURI, A. and CHRISTOFIDES, T. C. (2013). Indirect Questioning in Sample Surveys. Springer-Verlag, Heidelberg, Germany. · Zbl 1306.62024 [7] CHAUDHURI, A. and MUKERJEE, R. (1988). Randomized Response: Theory and Techniques. Marcel Dekker, New York. · Zbl 0643.62002 [8] ERIKSSON, SA, A new model for randomized response, Interenat. Stat. Rev., 41, 101-113, (1973) · Zbl 0287.92008 [9] GODAMBE, VP, A unified theory of sampling from finite populations, J. Roy. Statist. Soc., Ser B, 17, 269-278, (1955) · Zbl 0067.11406 [10] HANURAV, TV, Some aspects of unified sampling theory, Sankhya, Ser A, 28, 175-204, (1966) [11] HORVITZ, DG; THOMPSON, DJ, A generalization of sampling without replacement, J. Amer. Statist. Assoc., 47, 663-685, (1952) · Zbl 0047.38301 [12] RAJ, D; KHAMIS, SH, Some remarks on sampling with replacement, Ann. Math. Statist, 39, 550-557, (1958) · Zbl 0086.12404 [13] RAO, CR, Some theorems on minimum variance estimation, Sankhya, 12, 27-42, (1952) · Zbl 0049.10106 [14] SENGUPTA, S; KUNDU, D, Estimation of finite population Mean in randomized response surveys, J. Statist. Plann. Inference, 23, 117-125, (1989) · Zbl 0685.62015 [15] WARNER, SL, Randomized response - A survey technique for eliminating evasive answer bias, J. Amer. Statist. Assoc., 60, 63-69, (1965) · Zbl 1298.62024
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.