  In this article, we consider two forms of shrinkage estimators of the mean
$\theta$ of a multivariate normal distribution $X\sim N_{p}\left(\theta,
\sigma^{2}I_{p}\right)$ where $\sigma^{2}$ is unknown. We take the prior law
$\theta \sim N_{p}\left(\upsilon, \tau^{2}I_{p}\right)$ and we constuct a
Modified Bayes estimator $\delta_{B}^{\ast}$ and an Empirical Modified Bayes
estimator $\delta_{EB}^{\ast}$. 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.
