General Classes of Shrinkage Estimators for the Multivariate Normal Mean with Unknown Variance: Minimaxity and Limit of Risks Ratios
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Authors: A. BENKHALED AND A. HAMDAOUI
DOI: 10.46793/KgJMat2202.193B
Abstract:
In this paper, we consider two forms of shrinkage estimators of the mean ???? of a multivariate normal distribution X ∼ Np
in ℝp
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.
Keywords:
James-Stein estimator, multivariate Gaussian random variable, non-central chi-square distribution, quadratic risk, shrinkage estimator.
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