On shrinkage estimators improving the positive part of James-Stein estimator
In this work, we study the estimation of the multivariate normal mean by different classes of shrinkage estimators. The risk associated with the quadratic loss function is used to compare two estimators. We start by considering a class of estimators that dominate the positive part of James-Stein est...
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-12-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2021-0038 |
| Summary: | In this work, we study the estimation of the multivariate normal mean by different classes of shrinkage estimators. The risk associated with the quadratic loss function is used to compare two estimators. We start by considering a class of estimators that dominate the positive part of James-Stein estimator. Then, we treat estimators of polynomial form and prove if we increase the degree of the polynomial we can build a better estimator from the one previously constructed. Furthermore, we discuss the minimaxity property of the considered estimators. |
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| ISSN: | 2391-4661 |