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 
treatments in two-stage adaptive design. Suppose the effects of
two treatments have normal distributions with means 
and 
, respectively, and common
known variance 
. In the first stage, random samples of size 
with means
and 
are chosen from the two populations. Then the population with the
larger (or smaller) sample mean 
is selected, and a random sample of size
with mean 
is chosen from this population in the second stage of design.
Our aim is to estimate the mean 
(or 
) of the selected population based
on 
and 
in two-stage adaptive design under the reflected normal loss
function. We obtain minimax estimators of 
and 
, and then provide some
sufficient conditions for the inadmissibility of estimators of 
and 
. 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.
