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

Authors : Mehran NAGHİZADEH QOMİ, Nader NEMATOLLAHİ, Ahmad PARSİAN

Pages : 1109-1124

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Publication Date : 2015-10-01

Article Type : Research Paper

Abstract :Let  Π 1  and  Π 2  denote two gamma populations with common known shape parameter  α >  0  and unknown scale parameters  θ 1  and  θ 2 , re- spectively. Let  X 1  and  X 2  be two independent random variables from Π 1  and  Π 2 , and  X insert ignore into journalissuearticles values(1);  ≤  X insert ignore into journalissuearticles values(2);  denote the ordered statistics of  X 1  and X 2 . Suppose the population corresponding to the largest  X insert ignore into journalissuearticles values(2);  or the smallest  X insert ignore into journalissuearticles values(1);  observation is selected. This paper concerns on the ad- missible estimation of the scale parameters  θ M  and  θ J  of the selected population under reflected gamma loss function. We provide sufficient conditions for the inadmissibility of invariant estimators of  θ M  and  θ J  . The admissibility and inadmissibility of estimators in the class of lin- ear estimators of the form  cX insert ignore into journalissuearticles values(2);  and  dX insert ignore into journalissuearticles values(1);  are discussed. We apply our results on  k -Records, censored data and extend to a subclass of exponential family.
Keywords : Admissibility, Estimation after selection, Inadmissibility, Invariant estimators, Gamma distribution, Reflected gamma loss function, k Records data, Type II censoring