Geodesic
Limits of risks ratios of shrinkage estimators under the balanced loss function
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 3, pp. 301-312.

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In this paper we study the estimation of a multivariate normal mean under the balanced loss function. We present here a class of shrinkage estimators which generalizes the James-Stein estimator and we are interested to establish the asymptotic behaviour of risks ratios of these estimators to the maximum likelihood estimators (MLE). Thus, in the case where the dimension of the parameter space and the sample size are large, we determine the sufficient conditions for that the estimators cited previously are minimax.
Keywords: balanced Loss Function, James-Stein estimator, multivariate Gaussian random variable, non-central chi-square distribution, shrinkage estimators. 
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Mekki Terbeche; Abdelkader Benkhaled; Abdenour Hamdaoui. Limits of risks ratios of shrinkage estimators under the balanced loss function. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 3, pp. 301-312. http://geodesic.mathdoc.fr/item/JSFU_2021_14_3_a3/

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