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 |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2021-0038 |
| _version_ | 1818488010702848000 |
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| author | Hamdaoui Abdenour |
| author_facet | Hamdaoui Abdenour |
| author_sort | Hamdaoui Abdenour |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T16:45:38Z |
| format | Article |
| id | doaj.art-c9accaef23bc4472aeb212f907fb4035 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-12-10T16:45:38Z |
| publishDate | 2021-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-c9accaef23bc4472aeb212f907fb40352022-12-22T01:41:05ZengDe GruyterDemonstratio Mathematica2391-46612021-12-0154146247310.1515/dema-2021-0038On shrinkage estimators improving the positive part of James-Stein estimatorHamdaoui Abdenour0Department of Mathematics, University of Sciences and Technology, Mohamed Boudiaf, Oran, Laboratory of Statistics and Random Modelisations of Tlemcen University (LSMA), AlgeriaIn 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.https://doi.org/10.1515/dema-2021-0038james-stein estimatormultivariate normal distributionnon-central chi-square distributionquadratic loss functionshrinkage estimators62j0762c2062h10 |
| spellingShingle | Hamdaoui Abdenour On shrinkage estimators improving the positive part of James-Stein estimator Demonstratio Mathematica james-stein estimator multivariate normal distribution non-central chi-square distribution quadratic loss function shrinkage estimators 62j07 62c20 62h10 |
| title | On shrinkage estimators improving the positive part of James-Stein estimator |
| title_full | On shrinkage estimators improving the positive part of James-Stein estimator |
| title_fullStr | On shrinkage estimators improving the positive part of James-Stein estimator |
| title_full_unstemmed | On shrinkage estimators improving the positive part of James-Stein estimator |
| title_short | On shrinkage estimators improving the positive part of James-Stein estimator |
| title_sort | on shrinkage estimators improving the positive part of james stein estimator |
| topic | james-stein estimator multivariate normal distribution non-central chi-square distribution quadratic loss function shrinkage estimators 62j07 62c20 62h10 |
| url | https://doi.org/10.1515/dema-2021-0038 |
| work_keys_str_mv | AT hamdaouiabdenour onshrinkageestimatorsimprovingthepositivepartofjamessteinestimator |