Aníbal Areia
ABSTRACT
Studies will be matrix triplets (X,Dp,Dn), where the matrix X has a row per object and a column per variable, while Dp and Dn are weight matrices for objects and variables, respectively.
Given a series of studies (Xi,Dp,Dn),i=1,...,k, we condense the matrix triplets into the Ai = XiDpXtiDn, and use spectral analysis of matrix S = [Sij],i,j = 1,...,k, with Sij = tr(AiAjt) to study the series evolution.
When we have a series of studies for each treatment of a basis design we carry out an ANOVA-like inference to study the action of the factors in the base design on the evolution of the series associated to the differents treatments.
- Areia, Aníbal, Mexia, João and Oliveira, M. 2008. Models for a series of studies based on geometrical representation. Statistical Methodology 5, 277--288.Google Scholar
Cross Ref
- Ito, K. 1980. Robustness of Anova and Macanova Test Procedures. P. R. Krishnaiah (ed.), Handbook of Statistics, Vol. I, North Holland.Google Scholar
- Scheffé, H. 1959. The Analysis of Variance, John Wiley and Sons, New York.Google Scholar
- Areia, Aníbal and Oliveira, M. 2013. Longitudinal Analysis for Matched Series of Studies, AIP, Conf. Pr. 1558, 821--824.Google Scholar
- Areia, Aníbal and Oliveira, M. 2012. Transversal Analysis in Matched Series of Studies, AIP, Conf. Pr. 1479, 1670--1673.Google Scholar
- Lavit, C. 1988. Analyse Conjointe de Tableaux Quantitatifs. Collection Méthods + Programmes, Masson, Paris, 91--262.Google Scholar
- Mexia, João T. 1995. Inferência Estatística Linear, Centro de Estudos de Matemática Aplicada, Edições Universitárias Lusófonas, Lisboa.Google Scholar
Index Terms
- Inference for the Evolution in Series of Studies
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