Linear sufficiency with respect to a given vector of parametric functions
Let \(\{\) Y,X\(\beta\),V\(\}\) be a general Gauss-Markov model. FY is said to be linearly sufficient for the estimable function \(K\beta\) if the minimum dispersion linear unbiased estimator of \(K\beta\) is a linear function of FY. Theorem 1 gives a necessary and sufficient condition for such a linear sufficiency. Corollaries deal with some special cases, while theorem 2 considers the problem of linear minimal sufficiency. Applications are given to models with additional information on nuisance parameters, stepwise estimation and seemingly unrelated regressions.
minimum dispersion linear unbiased estimator
scientific article; zbMATH DE number 3994797
scientific article