University of TehranJournal of Sciences, Islamic Republic of Iran1016-110424220130601Estimating a Bounded Normal Mean
Under the LINEX Loss Function15716432082ENA.KarimnezhadDepartment of Statistics, Faculty of Mathematics, Statistics and Computer
Science, University of Tehran, Tehran, Islamic Republic of IranJournal Article20130118Let <em>X</em> be a random variable from a normal distribution with unknown mean <em>θ</em> and known variance <em>σ</em><sup>2</sup>. In many practical situations, <em>θ</em> is known in advance to lie in an interval, say [−<em>m</em>,<em>m</em>], for some <em>m</em> > 0. As the usual estimator of <em>θ</em>, i.e., <em>X</em> under the LINEX loss function is inadmissible, finding some competitors for <em>X</em> becomes worthwhile. The only study in the literature considered the problem of minimax estimation of <em>θ</em> 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 [−<em>m</em>,<em>m</em>] is proposed. Finally, considering risk performance as a comparison criterion, the estimators are compared and depending on the values taken by <em>θ</em> in the interval [−<em>m</em>,<em>m</em>], the appropriate estimator is suggested.
https://jsciences.ut.ac.ir/article_32082_f213688e182938621c667ee8a6906180.pdf