Maximum Likelihood and Least Squares Estimation of Linear Functional Relationships

Abstract

In this paper maximum likelihood and least squares estimatorsfor a generai version of the model of linear functional relationships are derived. This model arises if in a linear regression model the nonrandom regressors are known with random error only.

The model considered deals with the multivariate case; it covers cases of replication, dependent observations, different degrees of information on the covariance structure, special designs in the analysis of variance, homogeneous and inhomogeneous linear relations. Intermediate models not yet considered in the literature are included. In all cases at least maximum likelihood equations are given. Non-degeneracy of estimation results with probability one is established.