Assumption-Based Reasoning with Classical Regression Models

Abstract

In this chapter, a special class of Gaussian linear systems will be analyzed. When expressed in canonical coordinates, these systems turn out to be regular linear regression models, with the slight difference that the distribution of the error term is now assumed to be known (this is a general assumption of functional models). This assumption guarantees that the result of the inference is completely known. Of course, the analysis could be carried out in a similar way when the variance of the distribution of the error term is left unspecified. In this case, the result of the analysis will depend on this unspecified variance. The same remark also holds for any generalized functional model when the distribution of the random perturbation is unknown.