Generalized Linear Models with a Small Scale Parameter

We propose a study of asymptotic properties in an extension of the Nelder-Wedderburn generalized linear models (GLM) and we apply the results to a model choice in Mandel's models of analysis of variance (ANOVA). This study concerns the behaviour of the maximum likelihood estimators (MLE) when the scale parameter of the GLM tends to zero. Finally, to allow the use of our results, we give some specifications of this limit in three cases of the GLM.