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Algebraic structureof step nesting designs

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EN
Abstrakty
EN
Step nesting designs may be very useful since they require fewer observations than the usual balanced nesting models. The number of treatments in balanced nesting design is the product of the number of levels in each factor. This number may be too large. As an alternative, in step nesting designs the number of treatments is the sum of the factor levels. Thus these models lead to a great economy and it is easy to carry out inference. To study the algebraic structure of step nesting designs we introduce the cartesian product of commutative Jordan algebras.
Twórcy
  • Área Científica de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro, 01 1959-007 Lisboa, Portugal
autor
  • Área Científica de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro, 01 1959-007 Lisboa, Portugal
  • Departamento de Matemática, Faculdade de Cięncias e Tecnologia Universidade Nova de Lisboa, Monte de Caparica 2829-516 Caparica, Portugal
Bibliografia
  • [1] D. Cox and P. Salomon, Components of Variance, Chapman & Hall, New York 2003.
  • [2] H. Drygas and R. Zmyślony, Jordan algebras and Bayesian quadratic estimation of variance components, Linear Algebra and it's Applications 168 (1992), 259-275.
  • [3] P. Jordan, J. von Neumann and E. Wigner, On a algebraic generalization of the quantum mechanical formulation, The Annals of Mathematics 35-1, 2nd Ser. (1934), 29-64.
  • [4] J. Malley, Statistical Applications of Jordan Algebras, Springer-Verlag 2004.
  • [5] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310.
  • [6] A. Michalski and R. Zmyślony, Testing hypothesis for linear functions of parameters in mixed linear models, Tatra Mountain Mathematical Publications 1999.
  • [7] J. Nelder, The interpretation of negative components of variance, Biometrika 41 (1954), 544-548.
  • [8] C. Rao and M. Rao, Matrix Algebras and Its Applications to Statistics and Econometrics, World Scientific 1998.
  • [9] J. Seely, Linear spaces and unbiased estimaton, The Annals of Mathematical Statistics 41-5 (1970a), 1725-1734.
  • [10] J. Seely, Linear spaces and unbiased estimators - Application to the mixed linear model, The Annals of Mathematical Statistics 41-5 (1970b), 1735-1745.
  • [11] J. Seely, Quadratic subspaces and completeness, The Annals of Mathematical Statistics 42-2 (1971), 710-721.
  • [12] J. Seely and G. Zyskind, Linear Spaces and minimum variance estimation, The Annals of Mathematical Statistics 42-2 (1971), 691-703.
  • [13] J. Seely, Completeness for a family of multivariate normal distribution, The Annals of Mathematical Statistics 43 (1972), 1644-1647.
  • [14] J. Seely, Minimal suffcient statistics and completeness for multivariate normal families, Sankhya 39 (1977), 170-185.
  • [15] S. Silvey, Statistical Inference, CRC Monographs on Statistics & Applied Probability, Chapman & Hall 1975.
  • [16] D. Vanaleuween, J. Seely and D. Birkes, Sufficient conditions for orthogonal designs in mixed linear models, Journal of Statistical Planning and Inference 73 (1998), 373-389.
  • [17] D. Vanaleuween, D. Birkes and J. Seely, Balance and orthogonality in designs for mixed classification models, The Annals of Statistics 27-6 (1999), 1927-1947.
  • [18] R. Zmyślony, A characterization of best linear unbiased estimators in the general linear model, pp. 365-373 in: Mathematical Statistics and Probability Theory, Proc. Sixth Internat. Conf., Wisła, 1978, Lecture Notes in Statist., 2, Springer, New York-Berlin.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1129
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