On Estimation Following Selection with Applications on k-Records and Censored Data
Mehran Naghizadeh Qomi, Nader Nematollahi, Ahmad Parsian · Journal of the Iranian Statistical Society · 2010
Let X1 and X2 be two independent random variables from gamma populations Π1, Π2 with means αθ1 and αθ2 respectively, where α(> 0) is the common known shape parameter and θ1 and θ2 are scale parameters. Let X(1) ≤ X(2) denote the order statistics of X1 and X2. Suppose that the population corresponding to the largest X (2) (or the smallest X (1) ) observation is selected. The problem of interest is to estimate the scale parameters θM (and θJ ) of the selected gamma population under an asymmetric scale invariant loss function. We characterize admissible estimators of θM (or θJ ) within the class of linear estimators of the form cX(2) (or cX(1)). In estimating θM ,