Estimation Following Selection under LINEX Loss Function

Estimation Following Selection under LINEX Loss Function

Let Xi Xi . . . . . Xi i r 1, 2, be a pair of independent random samples from two exponential populations with unknown location parameters f; and common known scale parameter C. Let X, denote the minimum of the i-th sample, X(1) = min(X1, X2) and X) = max(X1, X). Suppose the population corresponding to the largest X (or the smallest X1) is selected. In this paper, we consider the estimation of the location parameters fat (and ty) of the selected exponential population under LINEX loss function. We characterize admissible estimators of daf (or ty) within the class of linear estimators of the form X) + c (or X(1) + c). we give sufficient conditions for minimaxity of estimators of 6. At and ty.