Distancia entre modelos lineales normales

Abstract

Este trabajo aborda el problema de comparar modelos lineales normales desde una perspectiva geométrica. A tal fin, se define una distancia geométrica informativa entre dos modelos lineales normales. La distancia propuesta es estudiada para diferentes condiciones experimentales. Se hallan además extensiones al modelo lineal normal multivariante. Finalmente, se deducen pruebas de significación para las distancias.

In this paper, starting from the Shannon's entropy functional we have defined and obtained algebraic expressions of distances between univariate and multivariate normal linear models of equal variance. We have explicitly obtained algebraic expressions of the estimators of such distances which have been used to design test of hypothesis between two or more univariate and multivariate normal linear models of equal variance, establishing its relation with the tests of hypothesis used in the Analysis of Variance. Advantages of using distances in hypothesis testing lie in the possibility of making graphical representations of the results, by means of representing the compared linear models on a graph {dendrogram or additive tree) or into an euclidean space of reduced dimension.