Minimaxity and Limits of Risks Ratios of Shrinkage Estimators of a Multivariate Normal Mean in the Bayesian Case

02/13/2020

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by   Abdenour Hamdaoui, et al.

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In this article, we consider two forms of shrinkage estimators of the mean θ of a multivariate normal distribution X∼ N_p(θ, σ^2I_p) where σ^2 is unknown. We take the prior law θ∼ N_p(υ, τ^2I_p) and we constuct a Modified Bayes estimator δ_B^∗ and an Empirical Modified Bayes estimator δ_EB^∗. We are interested in studying the minimaxity and the limits of risks ratios of these estimators, to the maximum likelihood estimator X, when n and p tend to infinity.