Study on multivariate Statistical models and their inference procedures for analysis of high-dimensional data and its applications

当变量的维度大于样本量时，考虑了多元实正态分布和复正态分布的大协方差阵的估计问题。给出了实和复数情形下奇异Wishart矩阵的Stein-Haff恒等式和特征结构的微积分。利用这些技巧，分别得到了不变二次损失函数下总体协方差阵的一类估计量的无偏风险估计。

The problem of estimating large covariance matrices of multivariate real normal and complex normal distributions is considered when the dimension of the variables is larger than the number of sample size. The Stein-Haff identities and calculus on eigenstructures for singular Wishart matrices are developed for real and complex cases, respectively. By using these techniques, the unbiased risk estimates for certain class of estimators for the population covariance matrices under an invariant quadratic loss functions are obtained for real and complex cases, respectively.