Let X 1 and X 2 be two independent random variables from normal populations Π1, Π2 with different unknown location parameters θ1 and θ2, respectively and common known scale parameter σ. Let X (2) = max (X 1, X 2) and X (1) = min (X 1, X 2). We consider the problem of estimating the location parameter θ M (or θ J ) of the selected population under the reflected normal loss function. We obtain minimax estimators of θ M and θ J . Also, we provide sufficient conditions for the inadmissibility of invariant estimators of θ M and θ J .
