A note on UMVU-estimation under randomized response model

Considering a class of randomized response trials for eliciting sensitive information from a sample survey and a class of ordered sampling designs, a uniformly minimum variance unbiased estimator of population variance (of the sensitive character) has been obtained. This note indicates that a theorem (theorem 3.9) of Cassel, Sarndal and Wretman (1917) and the results in the present note can be extended to estimation of any symmetric function of population values in the held of direct response surveys and randomized response surveys respectively.