Abstract: Let g(\cdot), W(\cdot) be non-negative decreasing function and non-negative inoreasing function, respectively. In this paper, we prove that If sample matrix X \sim L E C_n \times p\left(e_n \mu^\prime, I_n \otimes \Sigma, g\right), \mu, \Sigma>0 unknown, then under loss function W\left((d-\mu)^\prime \Sigma^-1(d-\mu)\right. ), sample mean \barx=\frac1n X^\prime e_n is minimax estimator for \mu. If x_1, \cdots, x_n are i.i.d.random vectors, x_i \sim E O_p\left(\mu, I_p, g\right), then under loss funotion W\left(\|d-\mu\|^2\right), \quad \barx=\frac1n \sum_j=1^n x_j is minimax estimator in \mathscrF, where \mathscrF=\\delta(\barx): \delta(\cdot) is a real function depending on \barx\. Some sequential minimax properties for sample mean and Stein two-stage ostimator are also considered.