Baranchick-type Estimators of a Multivariate Normal Mean Under the General Quadratic Loss Function
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https://elib.sfu-kras.ru/handle/2311/135903Author:
Hamdaoui, Abdenour
Benkhaled, Abdelkader
Terbeche, Mekki
Хамдауи, Абденур
Бенхалед, Абделькадер
Тербече, Мекки
Date:
2020-09Journal Name:
Журнал Сибирского федерального университета. Математика и физика, 2020. Journal of Siberian Federal University. Mathematics & Physics 2020, 13(5)Abstract:
The problem of estimating the mean of a multivariate normal distribution by different types
of shrinkage estimators is investigated. We established the minimaxity of Baranchick-type estimators
for identity covariance matrix and the matrix associated to the loss function is diagonal. In particular
the class of James-Stein estimator is presented. The general situation for both matrices cited above is
discussed Исследована проблема оценки среднего многомерного нормального распределения
различными типами оценок усадки. Мы установили минимаксность оценок типа Баранчика для
единичной ковариационной матрицы, а матрица, связанная с функцией потерь, является диагональной. В частности, представлен класс оценки Джеймса-Стейна. Обсуждается общая ситуация
для обеих упомянутых выше матриц
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