Consideration is given to minimum variance unbiased estimation when the choice of estimators is restricted to a finite-dimensional linear space. The discussion gives generalizations and minor extensions of known results in linear model theory utilizing both the coordinate-free approach of Kruskal and the usual parametric representations. Included are (i) a restatement of a theorem on minimum variance unbiased estimation by Lehmann and Scheffe; (ii) a minor extension of a theorem by Zyskind on best linear unbiased estimation; (iii) a generalization of the covariance adjustment procedure described by Rao; (iv) a generalization of the normal equations; and (v) criteria for existence of minimum variance unbiased estimators by means of invariant subspaces. Illustrative examples are included.
Justus Seely. George Zyskind. "Linear Spaces and Minimum Variance Unbiased Estimation." Ann. Math. Statist. 42 (2) 691 - 703, April, 1971. https://doi.org/10.1214/aoms/1177693418