A Generalized Least-Squares Approach to Linear Functional Relationships

Summary A linear functional relationship between mathematical variables is postulated. The problem considered is the estimation of this relationship given observed random variate values, various assumptions being made about the distribution of the departures of these from the corresponding mathematical variable values. The least-squares principle is generalized to deal with cases in which these departures are correlated. The bivariate case is considered in detail. Extension to p variates involves no new principle if only a single linear relationship is postulated. A simple application in growth studies is discussed.