ABSTRACT
Degree-one models can be applied to cross products matrices and Hilbert-Schmidt scalar products matrices. The latter have an important role in the first stage (inter-structure) of STATIS methodology, while the former matrices (in particular the AAt and AtA cross products, which have the same non-null eigenvalues) have an important role in inference. The case of rank one is interesting since the first eigenvector of matrix XXt may be used to describe the behavior of the variables corresponding to the columns of X. We now consider the estimators of the pair (λ, α) and testing that the mean matrix as rank one. We apply our results to cross product matrices XXt, given an numerical example
- Areia, A. 2009. Séries Emparelhadas de Estudos. Ph.D. Thesis, University of Évora, Évora.Google Scholar
- Oliveira, M. M. 2002. Modelação de Series Emparelhadas com Estrutura Comum. Ph.D. Thesis, University of Évora, Évora.Google Scholar
- Oliveira, M. M. & Mexia, J. T. 2004. AIDS in Portugal: endemic versus epidemic forecasting scenarios for mortality. International Journal Forecasting 20, 131--137.Google ScholarCross Ref
- Oliveira, M. M. & Mexia, J. T. 2007a. ANOVA like analysis of matched series of studies with a common structure. Journal of Statistical Planning and Inference, 137, 1862--1870.Google ScholarCross Ref
- Oliveira, M. M. & Mexia, J. T. 2007b. Modelling series of studies with a common structure. Computational Statistics & Data Analysis, 51, 5876--5885.series of studies with a common structure. Computational Statistics & Data Analysis, 51, 5876--5885. Google ScholarDigital Library
- Dias, C., Oliveira, M. M. & Mexia, J. T. 2012. Models of Symmetric Stochastic Matrices. Proceedings of the International Conference of Numerical Analysis and Applied Mathematics. Vol. 1479 (pp. 1666--1669).Google ScholarCross Ref
- Scheffé, H. 1959. The Analysis of Variance, New York: John Wiley & Sons, 1959Google Scholar
- P. K. Ito, P. K. 1980. Robustness of Anova and Macanova Test Procedures, P. R. Krishnaiah (ed), Handbook of Statistics1, Amsterdam: North Holland, pp. 199--236.Google Scholar
- Dias, C. 2013. Models and Families of Models for Symmetric Stochastic Matrices. Ph.D. Thesis, University of Évora, Évora.Google Scholar
- Mexia, J. T. 1995. Introdução à Inferência Estatística Linear. Centro de Estudos de Matemática Aplicada. Edições Universitárias Lusófonas: Lisboa.Google Scholar
- Oliveira, M., M. & Mexia, J., T. 1999. F Tests for Hypothesis on the Structure Vectors of Series. Discussiones Mathematicae, 19(2), 345--353.Google Scholar
- Oliveira, M. M. & Mexia J. 1999b. Multiple Comparisons for Rank one Common Structures. Biometrical Letters, 36(2), 159--167.Google Scholar
- Oliveira, M. M. & Mexia J. 1999a. F Tests for Hypothesis on the Structure Vectors of Series. Discussiones Mathematicae, 19(2), 345--353.Google Scholar
- Oliveira, M. M. 2002. Modelação de Series Emparelhadas com Estrutura Comum. Ph.D. Thesis, University of Évora, Évora.Google Scholar
- Dias, C. 2000. Análise Conjunta Pesada de Regressões. Master Thesis, University of Évora, Évora.Google Scholar
Index Terms
- Degree-one Models and Cross Product Matrices
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