Estimation of the Parameter of the Selected Binomial Population

Suppose we have p (p ⩾ 2) independent binomial Bin(1, θi) populations, where θi’s are unknown. Suppose the ith population is selected if where denotes the mean of a random sample of size ni from the population associated with θi. In this paper, we estimate the parameter of the selected population. It is shown that neither unbiased nor risk-unbiased estimators exist. When additional observations from the selected population are available, we obtain an unbiased, risk-unbiased, and the two-stage UMVCU estimators. The bias and the risk of the obtained estimators are compared through simulation.