Estimating a Bounded Normal Mean Relative to Squared Error Loss Function
Let be a random sample from a normal distribution with unknown mean and known variance The usual estimator of the mean, i.e., sample mean is the maximum likelihood estimator which under squared error loss function is minimax and admissible estimator. In many practical situations, is known...
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| Format: | Article |
| Language: | English |
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University of Tehran
2011-09-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
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| Online Access: | https://jsciences.ut.ac.ir/article_23589_c00c9b7bdf289e4d84aa381dfa227d26.pdf |
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| author | A. Karimnezhad |
| author_facet | A. Karimnezhad |
| author_sort | A. Karimnezhad |
| collection | DOAJ |
| description | Let be a random sample from a normal distribution with unknown mean and known variance The usual estimator of the mean, i.e., sample mean is the maximum likelihood estimator which under squared error loss function is minimax and admissible estimator. In many practical situations, is known in advance to lie in an interval, say for some In this case, the maximum likelihood estimator changes and dominates but it is no longer admissible. Minimax and some other estimators for this problem have been studied by some researchers. In this paper, a new estimator is proposed and the risk function of it is compared with some other competitors. According to our findings, the use of and the maximum likelihood estimator is not recommended when some information are accessible about the finite bounds on in advance. Based on the values taken by in , the appropriate estimator is suggested. |
| format | Article |
| id | doaj-art-cec4b2a58b9642bf9be60c78718cc26c |
| institution | Kabale University |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2011-09-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-cec4b2a58b9642bf9be60c78718cc26c2025-08-20T03:53:51ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142011-09-0122326727623589Estimating a Bounded Normal Mean Relative to Squared Error Loss FunctionA. Karimnezhad0Allameh Tabataba’i UniversityLet be a random sample from a normal distribution with unknown mean and known variance The usual estimator of the mean, i.e., sample mean is the maximum likelihood estimator which under squared error loss function is minimax and admissible estimator. In many practical situations, is known in advance to lie in an interval, say for some In this case, the maximum likelihood estimator changes and dominates but it is no longer admissible. Minimax and some other estimators for this problem have been studied by some researchers. In this paper, a new estimator is proposed and the risk function of it is compared with some other competitors. According to our findings, the use of and the maximum likelihood estimator is not recommended when some information are accessible about the finite bounds on in advance. Based on the values taken by in , the appropriate estimator is suggested.https://jsciences.ut.ac.ir/article_23589_c00c9b7bdf289e4d84aa381dfa227d26.pdfadmissibilitysquared error lossbounded normal meanmaximum likelihood estimatorrao-blackwellization |
| spellingShingle | A. Karimnezhad Estimating a Bounded Normal Mean Relative to Squared Error Loss Function Journal of Sciences, Islamic Republic of Iran admissibility squared error loss bounded normal mean maximum likelihood estimator rao-blackwellization |
| title | Estimating a Bounded Normal Mean Relative
to Squared Error Loss Function |
| title_full | Estimating a Bounded Normal Mean Relative
to Squared Error Loss Function |
| title_fullStr | Estimating a Bounded Normal Mean Relative
to Squared Error Loss Function |
| title_full_unstemmed | Estimating a Bounded Normal Mean Relative
to Squared Error Loss Function |
| title_short | Estimating a Bounded Normal Mean Relative
to Squared Error Loss Function |
| title_sort | estimating a bounded normal mean relative to squared error loss function |
| topic | admissibility squared error loss bounded normal mean maximum likelihood estimator rao-blackwellization |
| url | https://jsciences.ut.ac.ir/article_23589_c00c9b7bdf289e4d84aa381dfa227d26.pdf |
| work_keys_str_mv | AT akarimnezhad estimatingaboundednormalmeanrelativetosquarederrorlossfunction |