Auniversal Formula of Variance Component Estimation

A universal formula of variance component estimation by least squares is derived with the general functional model (the condition adjustment with unknown parameters and constraints among the parameters). The formulae based on the condition adjustment model or condition adjustment with unknowns are just special cases of the universal formula. Moreover, if the weight matrix is appropriately selected, both the MINQUE and Helmert formulae are its reduced version. In particularly, the conclusion is also holds for the BIQUE and MLE provided the inverse of the covariance matrix is taken as weight matrix. Additionally, the simplified formula is proposed and generalized. Hypothesis test theory of least squares variance component estimation is also extended.