Estimation associated with linear models: a revisitation

Abstract

The association of linear models with the analysis of complex sets of data dates back to Gauss (about 1800). But linear models assumed a major role in statistics only after Fisher's colleagues introduced then in explaining the analysis of variance. Sirica then it has become a common practice to describe experimental situations by associated linear models* The emergence of the concept of estiimability and its associated pedagogical difficulties accompa­nied this practice. This paper reconsiders the definition of a linear model with special reference to its association with the experimental context. The parameters of the resulting linear model submit to simple estimation without definitional ambiguity, These ideas are illustrated by considering the analy­sis of unbalanced cross classifications, a situation in which the definitional ambiguities of the usual linear models pose serious problems. Finally, the proposed model is compared to the usual less than full rank model.