On the Superadditivity of Information Matrices in Gauss-Markov Models.

摘要

The statistical efficiency of designs associated with the linear model is by and large measured solely on the basis of the information matrices. It is shown that when data from two experiments with the same model, which might contain nuisance parameters, but with possibly different design matrices are combined, then the resulting information matrix is larger (in the sense of nonnegative definiteness) than the sum of the individual information matrices. Cases where equality is achieved are completely characterized geometrically and statistically. Conditions where the best linear unbiased estimator of estimable functions are obtained as linear combination of the best linear unbiased estimators of the same function from the individual experiments are determined. (Author)