Generalized Bayes Minimax Estimators of the Multivariate Normal Mean with Unknown Covariance Matrix
协方差矩阵未知时多元正态均值的广义贝叶斯极小极大估计
Let $\mathbf{X}$ be a $p$-variate $(p \geqq 3)$ vector normally distributed with mean $\mathbf{\theta}$ and covariance matrix $\Sigma$, positive definite but unknown. Let $A$ be a $p \times p$ Wishart matrix with parameters $(n, \Sigma)$, independent of $\mathbf{X}$. To estimate $\mathbf{\theta}$ relative to quadratic loss function $(\hat{\mathbf{\theta}} - \mathbf{\theta})'\Sigma^{-1}(\hat{\mathbf{\theta}} - \mathbf{\theta})$, we obtain a family of minimax estimators $\mathbf{\delta}(\mathbf{X}, \mathbf{A})$…