Estimation of the Parameter of the Selected Binomial Population

Riyadh R. Al-Mosawi and P. Vellaisamy

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 22, 4796-4811

Abstract: Suppose we have p (p ⩾ 2) independent binomial Bin(1, θi) populations, where θi’s are unknown. Suppose the ith population is selected if Xi‾≥(or≤)Xj‾,∀j≠i,$\bar{X_i}\ge (\mbox{or}\le) \bar{X_j},\forall j\ne i,$ where X‾i$\bar{X}_i$ 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.

Date: 2015
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DOI: 10.1080/03610926.2013.799692

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