A General Theory of Estimation of Variance Covariance Components

Starting from the more general functional model and being based on their work of K. R. Koch (1986) and Ou Ziqiang (1989), marginal likelihood function of variance components is derived and is identical to the orthogonal complement likelihood function in this paper. Minimum norm quadratic unibiased estimator (MINQUE) is developed, which expands the formula by C. R. Rao (1973). It is proved that Helmert type estimation, MINQUE, BQUE and maximum likelihood estimation are identical to one another. Besides, a universal formula for accuracy evalution is presented. Through these work, the paper establishes a universal theory of variance covariance components.