CMA - Centro de Matemática e Aplicações da UBI
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CMA, Centre of Mathematics and Applications, is a research unit in Mathematics and Applications, hosted by University of Beira Interior (UBI). UBI provides the requested facilities, budget management, computing support and institutional framework to wards CMA’s activities.
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- Cross Additivity in Balanced Cross Nesting ModelsPublication . Ferreira, Sandra S.; Ferreira, Dário; Mexia, João T.Commutative Jordan Algebras were used to cary out inference for mixed models with balanced cross nesting in wich the variance componentes for interactions between sets of fixed effects and random effects are null.
- Double tier cross nesting design modelsPublication . Ferreira, Sandra S.; Ferreira, Dário; Mexia, João T.Inference is presented, first for balanced cross nesting models and then for the corresponding two tier models. These models are obtained nesting all the treatments of one model inside each treatment of the other model. An application is presented and the algebraic structure of the models is discussed using Commutative Jordan Algebras.
- Inference forLorthogonal modelsPublication . Ferreira, Sandra S.; Ferreira, Dário; Moreira, Elsa E.; Mexia, João T.We generalize the class of linear mixed models when normality is assumed.
- Exact Estimators for Normal Linear Mixed ModelsPublication . Ferreira, Sandra S.; Ferreira, Dário; Moreira, Elsa; Mexia, João T.
- Maximum Likelihood Estimation Methods for Variance Components in Linear Non-Orthogonal Small Size Design ModelsPublication . Ferreira, Dário; Ferreira, Sandra S.; Nunes, Célia; Mexia, João T.We compare four Maximum Likelihood Estimation methods for estimating variance components in normal linear mixed models, in the case of unbalanced small size design models: The Newton-Raphson, the Triple Minimization, the Gradient and a method where the starting points for the Newton-Raphson are the estimates obtained with the Triple Minimization method.
- Crossing Segregated Models with Commutative Orthogonal Block StructurePublication . Ferreira, Sandra S.; Ferreira, Dário; Nunes, Célia; Mexia, João T.; Simos, Theodore E.; Psihoyios, George; Tsitouras, Ch.A mixed model has segregation when its random effects part is segregated as a sub-model.We will show that under orthogonality condition, crossing segregated Commutative Orthogonal Block Structure (COBS) gives segregated COBS.
- Nesting Segregated Mixed ModelsPublication . Ferreira, Sandra S.; Ferreira, Sandra A. D.; Nunes, Célia; Mexia, João T.A mixed model has segregation when its random effects part is segregated as a sub-model. It will be shown that under orthogonality condition, nesting a random effects model inside a segregated mixed model or a segregated mixed model inside a fixed effects model the result will be a segregated mixed model. Unbiased estimators will be obtained for the variance components in both classes of models which are UMVUE, once normality is assumed.
- F Tests with Random Sample SizesPublication . Nunes, Célia; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.ANOVA is routinely used to compare pathologies. We now want to consider the case in which one of the pathologies is rare so that it may not be possible to know the dimension of the corresponding sample. In this case the distribution of the F test have random non-centrality parameters, when there are differences between the pathologies, and random degrees of freedom for the errors.
- Discriminant analysis and decision theoryPublication . Ferreira, Sandra Saraiva; Ferreira, Dário; Nunes, Célia; Mexia, João T.A unified approach, based in Statistical Decision Theory, is presented for Discriminant Analysis. Thus optimum allocation rules minimizing the expected costs are derived for the continuous case and for the mixed case. In the first case, the observed variables are continuous, while in the mixed case, there will also be discrete as qualitative variables. The second case has many times been treated using logistic regression. The breaking up of the allocation problem into distinct cases is now overcome.
- Orthogonal fixed effects ANOVA with random sample sizesPublication . Mexia, J. T.; Nunes, Célia; Ferreira, Dário; Ferreira, Sandra S.; Moreira, ElsaIn many relevant situations, such as in medical research, sample sizes may not be previously known. We extend ANOVA to those situations starting with one-way and then the general orthogonal situation. Sample sizes will be assumed to be random.