On the Admissibility of Horvitz-Thompson Strategies for Estimating Finite Population Proportions in Direct and Randomized Response Surveys

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Ramkrishnan (1975) had proved that in an open set-up any Horvitz-Thompson strategy for estimating a finite population mean of a quantitative variable is admissible within a class of comparable unbiased strategies. Sengupta and Kundu (1989) had proved a parallel result on the admissibility of similar strategies based on fixed size sampling designs under a randomized response model. In this paper we demonstrate that neither of these results is generally true for estimating a finite population proportion but some restricted versions of the results hold good.