Estimation of the Mean of the Selected Population

Let X i1, X i2, …,X in, i = 1, 2, be a pair of independent random samples from normal populations with means θi , and common known variance τ2. Suppose we select the population which provides the larger sample mean. In this article our main aim is to investigate different estimators for the mean of the selected population. Two different estimators are suggested by Sarkadi [9] and Putter and Rubinstein [8]. Two alternative estimators are suggested here and the bias and the mean square error of all the different types of estimators are tabled and compared.