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Advisor(s)
Abstract(s)
The models constituting a multiple model will correspond to d treatments of a base design.
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 \beta, l=1,...,d, 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 \tilde{\beta }(l) of \beta (l). l=1,...,d, have, approximately, the same covariance matrix. The eigenvectors of that matrix will give the principal estimable functions \epsilon_{i}^{\top} \beta (l) i=1,...,k, l=1,...,d, for the individual models. The ANOVA-like analysis will consider homologue components on principal estimable functions.
To apply our results we assume the factors in the base design to have fixed effects.
Moreover if w=1, and Z(1) has covariance matrix \sigma^{2} \m I_{n}, 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 \beta(l), l=1,...,d. An example of application of the proposed methodology is given.
Description
Keywords
ANOVA Cumulants Mixed Models
Citation
Patrícia Antunes, Sandra S. Ferreira, Dário Ferreira and João T. Mexia (2020). Multiple Additive Models. Communications in Statistics – Theory and Methods
Publisher
Marcel Dekker Inc.