Geodesic
On Minimaxity and Limit of Risks Ratio of James-Stein Estimator Under the Balanced Loss Function
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 3, p. 459

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The problem of estimating the mean of a multivariate normal distribution by different types of shrinkage estimators is investigated. Under the balanced loss function, we establish the minimaxity of the James-Stein estimator. When the dimension of the parameters space and the sample size tend to infinity, we study the asymptotic behavior of risks ratio of James-Stein estimator to the maximum likelihood estimator. The positive-part of James-Stein estimator is also treated.
Classification : 62F12 62C20, DOI
Keywords: Balanced loss function, James-Stein estimator, minimaxity, multivariate Gaussian random variable, non-central chi-square distribution, risk ratio, shrinkage estimator 
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Abdenour Hamdaoui; Abdelkader Benkhaled; Mekki Terbeche. On Minimaxity and Limit of Risks Ratio of James-Stein Estimator Under the Balanced Loss Function. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 3, p. 459 . http://geodesic.mathdoc.fr/item/KJM_2023_47_3_a9/