PROPERTIES OF THE INVERSE OF A NONCENTRAL WISHART MATRIX
PROPERTIES OF THE INVERSE OF A NONCENTRAL WISHART MATRIX
复制标题
非中心Wishart矩阵的逆矩阵的性质
作者：
G. Hillier;Raymond Kan
非中心Wishart矩阵的逆矩阵出现在多元统计工作的各种背景下，包括工具变量（IV）回归，但对其性质的研究很少。本文首先给出了非中心Wishart矩阵的逆的期望的表达式，然后对一些标量值函数的逆做了同样的工作。主要结果是通过利用简单但功能强大的群等方差性质的期望映射。随后的结果利用其他不变性的性质的后果。
The inverse of a noncentral Wishart matrix occurs in a variety of contexts in multivariate statistical work, including instrumental variable (IV) regression, but there has been very little work on its properties. In this paper, we first provide an expression for the expectation of the inverse of a noncentral Wishart matrix, and then go on to do the same for a number of scalar-valued functions of the inverse. The main result is obtained by exploiting simple but powerful group-equivariance properties of the expectation map involved. Subsequent results exploit the consequences of other invariance properties.