On estimating the scale parameter of the selected gamma population under the scale invariant squared error loss function

Let X1X1 and X2X2 be two independent random variables representing the populations Π1Π1 and Π2Π2, respectively, and suppose that the random variable XiXi has a gamma distribution with shape parameter p  , same for both the populations, and unknown scale parameter θi,i=1,2. Define, M=1M=1, if X1>X2,M=2, if X2>X1X2>X1 and J=3-MJ=3-M. We consider the component wise estimation of random parameters θMθM and θJθJ, under the scale invariant squared error loss functions L1(θ̲,δ1)=(δ1/θM-1)2 and L2(θ̲,δ2)=(δ2/θJ-1)2, respectively. Sufficient conditions for the inadmissibility of equivariant estimators of θMθM and θJθJ are derived. As a consequence, various natural estimators are shown to be inadmissible and better estimators are obtained.