PROPERTIES OF THE INVERSE OF A NONCENTRAL WISHART MATRIX

Grant Hillier and Raymond Kan

Econometric Theory, 2022, vol. 38, issue 6, 1092-1116

Abstract: 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.

Date: 2022
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