General Classes of Shrinkage Estimators for the Multivariate Normal Mean with Unknown Variance: Minimaxity and Limit of Risks Ratios

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DOI: 10.46793/KgJMat2202.193B


In this paper, we consider two forms of shrinkage estimators of the mean ???? of a multivariate normal distribution X Np(    2   )
 ????, σ Ip in p where σ2 is unknown and estimated by the statistic S2 (S2 σ2χn2). Estimators that shrink the components of the usual estimator X to zero and estimators of Lindley-type, that shrink the components of the usual estimator to the random variable X. Our aim is to improve under appropriate condition the results related to risks ratios of shrinkage estimators, when n and p tend to infinity and to ameliorate the results of minimaxity obtained previously of estimators cited above, when the dimension p is finite. Some numerical results are also provided.


James-Stein estimator, multivariate Gaussian random variable, non-central chi-square distribution, quadratic risk, shrinkage estimator.


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