Footnote:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments April 12, 2019 erstellt
Description:
The inverse of a noncentral Wishart matrix occurs in a variety of contexts in multivariate statistical work, including instrumental variables (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