Orthogonal models: Algebraic structure and explicit estimators for estimable vectors
Artur Pereira; Miguel Fonseca; João Tiago Mexia
Discussiones Mathematicae Probability and Statistics (2015)
- Volume: 35, Issue: 1-2, page 29-44
- ISSN: 1509-9423
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] A. Areia and F. Carvalho, Perfect families: an appliacation to orthogonal and error orthogonal models, AIP Conf. Proc. Numerical Analysis and Applied Mathematics: International Conferences of Numerical Analysis and Applied Mathematics 1558 (2013), 841-846.
- [2] T. Calinski and S. Kageyama, Block Designs: A Randomization Approach. Vol. I: Analysis , Lecture Notes in Statistics, Springer, 2000, 150.
- [3] T. Calinski and S. Kageyama, Block Designs: A Randomization Approach. Vol. II: Design, Lecture Notes in Statistics, Springer, 2003, 170.
- [4] F. Carvalho, J.T. Mexia and M.M. Oliveira, Canonic inference and commutative orthogonal block structure, Discuss. Math. Probab. and Stat. 28 (2) (2008), 171-181. Zbl1208.62093
- [5] F. Carvalho, J.T. Mexia and C. Santos, Commutative orthogonal block structure and error orthogonal models, Electronic Journal of Linear Algebra 25 (2013), 119-128. Zbl1283.15087
- [6] S.S. Ferreira, D. Ferreira, C. Fernandesa and J.T. Mexia, Orthogonal models and perfect families of symmetric matrices, Bulletin of the International Statistical Institute. Proc. ISI 2007, Lisboa 22-28 August (2007), 3252-3254.
- [7] M. Fonseca, J.T. Mexia and R. Zmyślony, Inference in normal models with commutative orthogonal block structure, Acta et Commentationes Universitatis Tartunesis de Mathematica (2008), 3-16. Zbl1166.62313
- [8] A. Houtman and T.P. Speed, Balance in designed experiments with orthogonal block structure, The annals of Statistics 11 (4) (1983), 1069-1085. Zbl0566.62065
- [9] E.L. Lehmann and G. Casela, Theory of Point estimation, 2nd ed. (Springer Tests Statistics, New York, Springer, 1998).
- [10] S. Mejza, On some aspects of general balance in designed experiments, Statistica 52 (1992), 263-278. Zbl0770.62060
- [11] J.T. Mexia, R. Vaquinhas, M. Fonseca and R. Zmyślony, COBS: segregation, matching, crossing and nesting, Latest Trends on Applied Mathematics, Simulation, Modelling (2010), 249-255.
- [12] J.A. Nelder, The analysis of randomized experiments with orthogonal block structure and the null analysis of variance, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 283 (1393), 147-162. Zbl0124.10703
- [13] J.A. Nelder, The analysis of randomized experiments with orthogonal block structure II. Treatment structure and the general analysis of variance, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 283 (1393), 163-178. Zbl0124.10703
- [14] J.R. Schott, Matrix Analysis for Statistics (Wiley Series in Probability and Statistics, 1997). Zbl0872.15002
- [15] J. Seely, Quadratic subspaces and completeness, The Annals of Mathematical Statistics 42 (1971), 710-721. Zbl0249.62067
- [16] D.M. Vanleeuwen, D.S. Birks, J.F. Seely, J. Mills, J.A. Greenwood and C.W. Jones, Sufficient conditions for orthogonal designs in mixed linear models, Journal of Statistics Planning and Inference 73 (1998), 373-389.
- [17] R. Zmyślony, A characterization of the best linear unbiased estimators in the general linear model, Lecture Notes Statistics 2 (1978), 365-373.