Best quadratic unbiased estimation of the variance matrix in normal regression

Abstract

In 1973 Balestra examined the linear model y=XB+u, where u is a normally distributed disturbance vector, with variance matrix Ω. Ω has spectral decomposition$\sum\limits_{i = 1}^r {\lambda _i M_i }$, and the matrices M_i are known.

Estimation of ω is thus equivalent with estimation of the λ_i. Balestra presented the best quadratic unbiased estimator of λ_i. In the present paper a derivation will be given which is based on a procedure developed by this writer (1980).