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Admissible and Minimax Estimation of the Parameters of the Selected Normal Population in Two-Stage Adaptive Designs Under Reflected Normal Loss Function

Mazarei Hasan, Nematollahi Nader

Probability and Mathematical Statistics

2019

Vol. 39, Fasc. 2

361--383

In clinical research, one of the key problems is to estimate the effect of the best treatment among the given k treatments in two-stage adaptive design. Suppose the effects of two treatments have normal distributions with means θ1 and θ2, respectively, and common known variance σ2. In the first stage, random samples of size n1 with means X1 and X2 are chosen from the two populations. Then the population with the larger (or smaller) sample mean XM is selected, and a random sample of size n2 with mean YM is chosen from this population in the second stage of design. Our aim is to estimate the mean θM (or θJ) of the selected population based on XM and YM in two-stage adaptive design under the reflected normal loss function. We obtain minimax estimators of θM and θJ, and then provide some sufficient conditions for the inadmissibility of estimators of θM and θJ. Theoretical results are augmented with a simulation study as well as a real data application.