%0 Journal Article
%T Estimating a Bounded Normal Mean
Under the LINEX Loss Function
%J Journal of Sciences, Islamic Republic of Iran
%I University of Tehran
%Z 1016-1104
%A Karimnezhad, A.
%D 2013
%\ 06/01/2013
%V 24
%N 2
%P 157-164
%! Estimating a Bounded Normal Mean
Under the LINEX Loss Function
%K Admissibility
%K Bayes estimator
%K LINEX loss function
%K Maximum Likelihood Estimator
%K Normal distribution
%R
%X Let X be a random variable from a normal distribution with unknown mean θ and known variance σ2. In many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. As the usual estimator of θ, i.e., X under the LINEX loss function is inadmissible, finding some competitors for X becomes worthwhile. The only study in the literature considered the problem of minimax estimation of θ In this paper, by constructing a dominating class of estimators, we show that the maximum likelihood estimator is inadmissible. Then, as a competitor, the Bayes estimator associated with a uniform prior on the interval [−m,m] is proposed. Finally, considering risk performance as a comparison criterion, the estimators are compared and depending on the values taken by θ in the interval [−m,m], the appropriate estimator is suggested.
%U https://jsciences.ut.ac.ir/article_32082_f213688e182938621c667ee8a6906180.pdf