On admissibility and inadmissibility of estimators after selection under reflected gamma loss function

Abstract

Let Π1 and Π2 denote two gamma populations with common known shape parameter α > 0 and unknown scale parameters θ1 and θ2, re- spectively. Let X1 and X2 be two independent random variables fromΠ1 and Π2, and X(1) ≤ X(2) denote the ordered statistics of X1 andX2. Suppose the population corresponding to the largest X(2) or the smallest X(1) observation is selected. This paper concerns on the ad- missible estimation of the scale parameters θM and θJ of the selected population under reflected gamma loss function. We provide sufficient conditions for the inadmissibility of invariant estimators of θM and θJ . The admissibility and inadmissibility of estimators in the class of lin- ear 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.