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Contents of PMS, Vol. 39, Fasc. 7,
pages 361 - 383
DOI: 10.19195/0208-4147.39.2.7
 

ADMISSIBLE AND MINIMAX ESTIMATION OF THE PARAMETERS OF THE SELECTED NORMAL POPULATION IN TWO-STAGE ADAPTIVE DESIGNS UNDER REFLECTED NORMAL LOSS FUNCTION

Hasan Mazarei
Nader Nematollahi

Abstract: 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 θ
 1  and θ
 2  , respectively, and common known variance σ2  . In the first stage, random samples of size n
 1  with means X¯
  1 and X¯
  2  are chosen from the two populations. Then the population with the larger (or smaller) sample mean X¯
  M  is selected, and a random sample of size n
 2  with mean Y¯
 M  is chosen from this population in the second stage of design. Our aim is to estimate the mean θ
 M  (or θ
 J  ) of the selected population based on ¯X
 M  and ¯Y
 M  in two-stage adaptive design under the reflected normal loss function. We obtain minimax estimators of θ
M  and θ
 J  , and then provide some sufficient conditions for the inadmissibility of estimators of θ
 M  and θ
 J  . Theoretical results are augmented with a simulation study as well as a real data application.

2000 AMS Mathematics Subject Classification: Primary: 62F10, 62F07; Secondary: 62C15, 62C20.

Keywords and phrases: Inadmissible estimator, minimax estimator, reflected normal loss function, two-stage adaptive design.

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