Multiple additive models

The models constituting a multiple model will correspond to d treatments of a base design. When we have individual additive models (Formula presented.) with (Formula presented.) independent, with (Formula presented.) independent components, with (Formula presented.) the (Formula presented.) th order cumulants, (Formula presented.) 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 (Formula presented.) (Formula presented.) 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 (Formula presented.) of (Formula presented.) (Formula presented.) have, approximately, the same covariance matrix. The eigenvectors of that matrix will give the principal estimable functions (Formula presented.) (Formula presented.) (Formula presented.) 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 (Formula presented.) and (Formula presented.) has covariance matrix (Formula presented.) 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 (Formula presented.) An example of application of the proposed methodology is given.