On estimating the mean of the selected normal population in two-stage adaptive designs

Adaptive design is widely used in clinical trials. In this paper, we consider the problem of estimating the mean of the selected normal population in two-stage adaptive designs. Under the LINEX and L2 loss functions, admissibility and minimax results are derived for some location invariant estimators of the selected normal mean. The naive sample mean estimator is shown to be inadmissible under the LINEX loss function and to be not minimax under both loss functions.

► Inadmissibility condition is provided for a class of general estimators in Theorem 2.1.
► As a special case of Theorem 2.1, the naive estimator μ^τ=ωX¯tau+(1−ω)Y¯ for some ω∈(0,1]ω∈(0,1] is shown to be inadmissible through Theorem 2.2.
► Minimax property of the naive estimator is derived under L2 loss function in Theorem 3.1 and LINEX loss function in Theorem 3.2.