Some puzzles appearing in statistical inference

Seyf Alemam; Hazhir Homei; Saralees Nadarajah

doi:10.5802/crmath.636

Article de recherche - Statistiques

Some puzzles appearing in statistical inference
[Quelques énigmes apparaissant dans l’inférence statistique]

Seyf Alemam ¹ ; Hazhir Homei ¹ ; Saralees Nadarajah ²

¹ Department of Statistics, University of Tabriz, P. O. Box 51666-17766, Tabriz, Iran
² Department of Mathematics, University of Manchester, Manchester M13 9PL, UK

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1243-1252.

Résumé
Abstract

Le théorème de Rao-Blackwell est largement connu pour être une technique mathématique puissante qui peut être utilisée pour améliorer la précision d’un estimateur. La procédure consiste à exploiter une statistique suffisante pour obtenir un estimateur amélioré ou un estimateur sans biais à variance uniformément minimale. Nous présentons ici une modification des statistiques suffisantes qui peut être appliquée au théorème de Rao-Blackwell ainsi que quelques applications fructueuses qui illustrent ses propriétés. De plus, certains théorèmes ont été réécrits dans le cadre de l’inférence statistique.

Rao-Blackwell theorem is widely known to be a mathematically powerful technique that can be used to improve the precision of an estimator. The procedure entails exploiting a sufficient statistic to obtain an improved estimator or a uniformly minimum variance unbiased estimator. A modification of sufficient statistics is introduced here which can be applied for Rao-Blackwell theorem along with some fruitful applications that illustrate its properties. Also some theorems have been rewritten in statistical inference.

Reçu le : 2023-04-18
Accepté le : 2024-03-31
Publié le : 2024-11-05

DOI : 10.5802/crmath.636

Classification : 62F10, 62F99
Keywords: Complete minimal sufficient statistic, Incomplete minimal sufficient statistic, Minimal sufficient statistic, Rao–Blackwell theorem, Sufficient statistic
Mot clés : Statistique suffisante minimale complète, statistique suffisante minimale incomplète, statistique suffisante minimale, théorème de Rao–Blackwell, statistique suffisante

Affiliations des auteurs :

Seyf Alemam ¹ ; Hazhir Homei ¹ ; Saralees Nadarajah ²

¹ Department of Statistics, University of Tabriz, P. O. Box 51666-17766, Tabriz, Iran
² Department of Mathematics, University of Manchester, Manchester M13 9PL, UK

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Some puzzles appearing in statistical inference},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1243--1252},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.636},
     language = {en},
}

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Seyf Alemam; Hazhir Homei; Saralees Nadarajah. Some puzzles appearing in statistical inference. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1243-1252. doi : 10.5802/crmath.636. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.636/

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