The estimation of a multivariate linear relation

A multivariate linear relation [eta]n = [beta]0[xi]n is considered, in which [xi]n and [eta]n are observed subject to white noise errors, with covariance matrices [sigma]0, [omega]0 respectively. If their elements lie in the null space of a suitable vector function, [beta]0, [sigma]0, [omega]0 may be uniquely defined by second-order functions of the data. The asymptotic properties of estimates of [beta]0, [sigma]0, [omega]0 are established under relatively mild conditions. We explore the possibility that explicit formulas for consistent estimates of [beta]0, [sigma]0, [omega]0 may be available.