Generalizations of Rao–Blackwell and Lehmann–Scheffé Theorems with Applications
Our aim in this paper is extending the applicability domain of the Rao–Blackwell theorem, our methodology is using conditional expectation and generalizing sufficient statistics, and one result is a generalization of the Lehmann–Scheffé theorem; as a conclusion, some problems that could not be solve...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/19/4146 |
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| author | Seyf Alemam Hazhir Homei Saralees Nadarajah |
| author_facet | Seyf Alemam Hazhir Homei Saralees Nadarajah |
| author_sort | Seyf Alemam |
| collection | DOAJ |
| description | Our aim in this paper is extending the applicability domain of the Rao–Blackwell theorem, our methodology is using conditional expectation and generalizing sufficient statistics, and one result is a generalization of the Lehmann–Scheffé theorem; as a conclusion, some problems that could not be solved by an earlier version of the Lehmann–Scheffé theorem become solvable by our new generalization. |
| first_indexed | 2024-03-10T21:40:11Z |
| format | Article |
| id | doaj.art-d05f914d371a412e94b3ed2962060a4b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:40:11Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d05f914d371a412e94b3ed2962060a4b2023-11-19T14:43:59ZengMDPI AGMathematics2227-73902023-09-011119414610.3390/math11194146Generalizations of Rao–Blackwell and Lehmann–Scheffé Theorems with ApplicationsSeyf Alemam0Hazhir Homei1Saralees Nadarajah2Department of Statistics, University of Tabriz, P.O. Box 51666-17766, Tabriz 51666-16471, IranDepartment of Statistics, University of Tabriz, P.O. Box 51666-17766, Tabriz 51666-16471, IranDepartment of Mathematics, University of Manchester, Manchester M13 9PL, UKOur aim in this paper is extending the applicability domain of the Rao–Blackwell theorem, our methodology is using conditional expectation and generalizing sufficient statistics, and one result is a generalization of the Lehmann–Scheffé theorem; as a conclusion, some problems that could not be solved by an earlier version of the Lehmann–Scheffé theorem become solvable by our new generalization.https://www.mdpi.com/2227-7390/11/19/4146complete minimal sufficient statisticincomplete minimal sufficient statisticminimal sufficient statisticRao–Blackwell theoremsufficient statistic |
| spellingShingle | Seyf Alemam Hazhir Homei Saralees Nadarajah Generalizations of Rao–Blackwell and Lehmann–Scheffé Theorems with Applications Mathematics complete minimal sufficient statistic incomplete minimal sufficient statistic minimal sufficient statistic Rao–Blackwell theorem sufficient statistic |
| title | Generalizations of Rao–Blackwell and Lehmann–Scheffé Theorems with Applications |
| title_full | Generalizations of Rao–Blackwell and Lehmann–Scheffé Theorems with Applications |
| title_fullStr | Generalizations of Rao–Blackwell and Lehmann–Scheffé Theorems with Applications |
| title_full_unstemmed | Generalizations of Rao–Blackwell and Lehmann–Scheffé Theorems with Applications |
| title_short | Generalizations of Rao–Blackwell and Lehmann–Scheffé Theorems with Applications |
| title_sort | generalizations of rao blackwell and lehmann scheffe theorems with applications |
| topic | complete minimal sufficient statistic incomplete minimal sufficient statistic minimal sufficient statistic Rao–Blackwell theorem sufficient statistic |
| url | https://www.mdpi.com/2227-7390/11/19/4146 |
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