Document Type : Original Paper

Author

• A. Karimnezhad

Department of Statistics, Faculty of Mathematics, Statistics and Computer Science, University of Tehran, Tehran, Islamic Republic of Iran

Abstract

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.
 

Keywords

• Admissibility
• Bayes estimator
• LINEX loss function
• Maximum Likelihood Estimator
• Normal distribution