Estimation of a Mean of a Normal Distribution with a Bounded Coefficient of Variation
The estimation of a mean of a normal distribution with an unknown variance is addressed under the restriction that the coefficient of variation is within a bounded interval. The paper constructs a class of estimators improving upon the best location-scale equivariant estimator of the mean. It is dem...
| Veröffentlicht in: | Sankhyā: The Indian Journal of Statistics (2003-2007). - Indian Statistical Institute, 1933. - 67(2005), 3, Seite 499-525 |
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| 1. Verfasser: | |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2005
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| Zugriff auf das übergeordnete Werk: | Sankhyā: The Indian Journal of Statistics (2003-2007) |
| Schlagworte: | Primary 62C10 Secondary 62C20 Secondary 62F10 Bounded mean Coefficient of variation Decision theory Generalized Bayes estimator Location-scale family Minimaxity Restricted parameters mehr... |
| Zusammenfassung: | The estimation of a mean of a normal distribution with an unknown variance is addressed under the restriction that the coefficient of variation is within a bounded interval. The paper constructs a class of estimators improving upon the best location-scale equivariant estimator of the mean. It is demonstrated that the class includes three typical estimators: the generalized Bayes estimator based on the uniform prior over the restricted region, the generalized Bayes estimator based on the prior putting mass on the boundary, and a truncated estimator. The non-minimaxity of the best location-scale equivariant estimator is shown in the general location-scale family. When another type of restriction is considered, however, we have a different story that the best location-scale equivariant estimator remains minimax. |
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| ISSN: | 09727671 |