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We study the estimation of the mean of a multivariate normal distribution N p , 2 I p in p , 2 is unknown and estimated by the chi-square variable S 2 2 n 2 . In this work we are interested in studying bounds and limits of risk ratios of shrinkage estimators to the maximum likelihood estimator, when n and p tend to infinity provided that lim p 2 p 2 c. The risk ratio for this class of estimators has a lower bound B m c 1 c , when n and p tend to infinity provided that lim p 2 p 2 c. We givedoi:10.15672/hjms.2014377624 fatcat:jnj4mzzkmjdv7bx2fyqqd7y5my