PROPERTIES OF THE INVERSE OF A NONCENTRAL WISHART MATRIX
研究了非中心Wishart矩阵逆的期望及其标量值函数的性质，对工具变量回归等多元统计应用有参考价值。
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.