Multiple Additive Models

The models constituting a multiple model will correspond to d treatments of a base design. When we have individual additive models with independent, with independent components, with the th order cumulants, the multiple model will be additive. Using a classic result on cumulant generation function we show how to obtain least square estimators for cumulants and generalized least squares estimators for vectors in the individual models. Next we carry out ANOVA-like analysis for the action of the factors in the base design. This is possible since the estimators of have, approximately, the same covariance matrix. The eigenvectors of that matrix will give the principal estimable functions for the individual models. The ANOVA-like analysis will consider homolog components on principal estimable functions. To apply our results we assume the factors in the base design to have fixed effects. Moreover if and has covariance matrix our treatment generalizes that previously given for multiple regression designs. In them we have a linear regression for each treatment of a base design. We then study the action of the factors on that design on the vectors An example of application of the proposed methodology is given.