On Minimaxity and Limit of Risks Ratio of James-Stein Estimator Under the Balanced Loss Function
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Authors: A. HAMDAOUI, A. BENKHALED AND M. TERBECHE
DOI: 10.46793/KgJMat2303.459H
Abstract:
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.
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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