The paper consists of two parts. The first part deals with solutions to some optimization problems. The general problem is one of minimssing Tr AVA′U, where V and U are positive definite matrices when the elements of the matrix are subject to linear restrictions of the type AX = O or X′AX = O and trace AVi = pi, i = 1,..., k, or U1′AU1 + ... + Uk′AUk = M. These results are used in determining Minimum Norm Quadratic Unbiased Estimators (MINQUE) of variance and covariance components in linear models. The present paper is a generalization of an earlier attempt by the author to obtain estimators of heteroscedastic variances in a regression model. The method is quite general, applicable to all experimental situations, and the computations are simple. © 1971.
Rao, C. R. (1971). Estimation of variance and covariance components-MINQUE theory. Journal of Multivariate Analysis, 1(3), 257–275. https://doi.org/10.1016/0047-259X(71)90001-7