A new criterion for determining the estimability of linear combinations of the parameters of a linear model is established. The result consists of evaluating the trace of a matrix and thus only one number must be checked to determine estimability. The sums of squares necessary to test hypotheses about estimable linear combinations are also derived. Finally, a stepwise computational procedure to compute generalized inverses and matrix products involving generalized inverses is presented. Using the theory and computational techniques, a computer program can be developed to provide a complete analysis of the linear model using generalized inverses.
George A. Milliken. "New Criteria for Estimability for Linear Models." Ann. Math. Statist. 42 (5) 1588 - 1594, October, 1971. https://doi.org/10.1214/aoms/1177693157