Estimating a Bounded Normal Mean Under the LINEX Loss Function
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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
University of Tehran
2013-06-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Subjects: | |
| Online Access: | https://jsciences.ut.ac.ir/article_32082_f213688e182938621c667ee8a6906180.pdf |
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| Summary: | 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. |
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| ISSN: | 1016-1104 2345-6914 |