The theory of generalized least-squares is reformulated here using the notion of generalized means. The generalized least-squares problem seeks a line which minimizes the average generalized mean of the square deviations in x and y. The notion of a generalized mean is equivalent to the generating function concept of the previous papers but allows for a more robust understanding and has an already existing literature. Generalized means are applied to the task of constructing more examples, simplifying the theory, and further classifying generalized least-squares regressions.
N. Greene. "Generalized Least-Squares Regressions IV: Theory and Classification Using Generalized Means,” in Mathematics and Computers in Science and Industry, 2014, pp. 19-35.