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FC - DM | Documentos por Auto-Depósito

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http://hdl.handle.net/10400.6/4101
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Browsing FC - DM | Documentos por Auto-Depósito by Author "Antunes, Patrícia"

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  • Estimation in additive models and ANOVA-like applications
    Publication . Antunes, Patrícia; Ferreira, Sandra S.; Ferreira, Dário; Nunes, Célia; Mexia, João T.
    A well-known property of cumulant generating function is used to estimate the first four order cumulants, using least-squares estimators. In the case of additive models, empirical best linear unbiased predictors are also obtained. Pairs of independent and identically distributed models associated with the treatments of a base design are used to obtain unbiased estimators for the fourth-order cumulants. An application to real data is presented, showing the good behaviour of the least-squares estimators and the great flexibility of our approach.
    2020Journal article Open access Show more
  • Multiple Additive Models
    Publication . Antunes, Patrícia; Ferreira, Sandra S.; Ferreira, Dário; Mexia, João T.
    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.
    2020Journal article Restricted access Show more