Weighted least-squares estimators of parametric functions of the regression coefficients under a general linear model

摘要

The weighted least-squares estimator of parametric functions K beta under a general linear regression model {y, X beta, sigma(2)Sigma} is defined to be K (beta) over cap, where (beta) over cap is a vector that minimizes (y - X beta)'V(y - X beta) for a given nonnegative definite weight matrix V. In this paper, we study some algebraic and statistical properties of K (beta) over cap and the projection matrix associated with the estimator, such as, their ranks, unbiasedness, uniqueness, as well as equalities satisfied by the projection matrices.