BEST UNBIASED LINEAR ESTIMATION, A COORDINATE FREE
APPROACH
S. Gnot
W. Klonecki
R. Zmyślony
Abstract: This paper gives further developments of the theory of uniformly minimum variance
unbiased estimation (UMVUE) in Euclidean vector spaces as originated by W.
Kruskal, G. Zyskind and J. Seely. It gives necessary and sufficient conditions for
the existence of a UMVUE for each estimable function in any subspace of linear
estimators with no restrictions posed on the covariance operators. Also construction of
UMVUE’s in a given subspace of linear estimators, if they exist, is considered. The
developed theory is illustrated by two examples: estimation of variance components in a
general mixed linear model and estimation of the mean in a multivariate linear model.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -