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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
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