- Hacettepe Journal of Mathematics and Statistics
- Vol: 44 Issue: 5
- On admissibility and inadmissibility of estimators after selection under reflected gamma loss functi...
On admissibility and inadmissibility of estimators after selection under reflected gamma loss function
Authors : Mehran Naghizadeh Qomi, Nader Nematollahi, Ahmad Parsian
Pages : 1109-1124
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Publication Date : 2015-10-01
Article Type : Research
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 (1) ≤ 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 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 (2) and dX (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