Let $\Pi_1$ and $\Pi_2$ denote two gamma populations with common known shape parameter $\alpha>0$ and unknown scale parameters $\theta_1$ and $\theta_2$, respectively. Let $X_1$ and $X_2$ be two independent random variables from $\Pi_1$ and $\Pi_2$, and $X_{(1)}\leq X_{(2)}$ denote the ordered statistics of $X_1$ and $X_{2}$. Suppose the population corresponding to the largest $X_{(2)}$ or the smallest $X_{(1)}$ observation is selected. This paper concerns on the admissible estimation of the scale parameters $\theta_M$ and $\theta_J$ of the selected population under reflected gamma loss function. We provide sufficient conditions for the inadmissibility of invariant estimators of $\theta_M$ and $\theta_J$. The admissibility and inadmissibility of estimators in the class of linear estimators of the form $cX_{(2)}$ and $dX_{(1)}$ are discussed. We apply our results on $k$-Records, censored data and extend to a subclass of exponential family.
