抄録
Let X and Y be sample means drawn from two independent normal distributions with unknown mean μi and known variance σ2i for i=1, 2, respectively, and let μ*≡max(μ1, μ2). The purpose of the present paper is to propose a new estimator of μ* as a hybrid estimator η(C) with a given non-negative C, which includes both estimators, an estimator η1 of a linear combination of X and Y and a simple estimator η2=max(X, Y). After comparing η(C) numerically with the maximum likelihood estimator δ given by Blumenthal and Cohen (1968b), it is found that η(C) is better than δ for C∈[1.87, 1.91] in view of the mean square error. The C has also been investigated in the sense of minimax regret, and an optimal C is obtained numerically as C*=1.704.
