Dergiler / Hacettepe Journal of Mathematics and Statistics / 2016 / Cilt: 45 - Sayı: 2

Estimation and orthogonal block structure

Sayfa
541–548
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The study observations of these estimators uses commutative Jordan Algebras, CJA, and extends the one given for a more restricted class of models, the models with commutative orthogonal block structure, COBS, in which the orthogonal projection matrix on the space spanned by the means vector commute with all variance-covariance matrices, see [7].

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Estimators with good behaviors for estimable vectors and variance components are obtained for a class of models that contains the well known models with orthogonal block structure, OBS, see [15], [16] and [1], [2].
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Temel Bulgular & Veri:Estimators with good behaviors for estimable vectors and variance components are obtained for a class of models that contains the well known models with orthogonal block structure, OBS, see [15], [16] and [1], [2].
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Sonuç & Katkı:The study observations of these estimators uses commutative Jordan Algebras, CJA, and extends the one given for a more restricted class of models, the models with commutative orthogonal block structure, COBS, in which the orthogonal projection matrix on the space spanned by the means vector commute with all variance-covariance matrices, see [7].
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:BLUE · LSE · OBS

Abstract

Estimators with good behaviors for estimable vectors and variance components are obtained for a class of models that contains the well known models with orthogonal block structure, OBS, see [15], [16] and [1], [2]. The study observations of these estimators uses commutative Jordan Algebras, CJA, and extends the one given for a more restricted class of models, the models with commutative orthogonal block structure, COBS, in which the orthogonal projection matrix on the space spanned by the means vector commute with all variance-covariance matrices, see [7].

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Bu Makaleye Atıf Yap

Ferreira, S. S., Moreira, E., Nunes, C., Ferreira, D., Mexiak, J. T. (2022). Estimation and orthogonal block structure. Hacettepe Journal of Mathematics and Statistics, Cilt: 45 - Sayı: 2, 541–548. https://ajindex.com/articles/530066

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Kaynakça (13)

  1. Caliński, T., Kageyama, S. Block Designs: A Randomization Approach, Volume I: Analysis, Lect. Notes Stat. 150, Springer, New York, 2000. Caliński, T., Kageyama, S. Block Designs: A Randomization Approach, Volume II: Design, Lect. Notes Stat., 170, Springer, New York, 2003.
  2. Carvalho, F., Mexia, J.T., Oliveira, M. Canonic inference and commutative orthogonal block structure. Discuss. Math. Probab. Stat., 28, 171-181, 2008.
  3. Ferreira, S.S., Ferreira, D., Fernandes, C., Mexia, J.T. Orthogonal Mixed Models and Perfect Families of Symmetric Matrices, Book of Abstracts, 56-th Session of the International Statistical Institute, ISI, Lisboa, 2007.
  4. Fonseca, M., Mexia, J.T., Zmyślony, R. Binary operations on Jordan algebras and orthogonal normal models, Linear Algebra Appl., 417, 75-86, 2006. 548 Fonseca, M., Mexia, J.T., Zmyślony, R. Jordan algebras, generating pivot variables and orthogonal normal models, J. Interdiscip. Math., 10(2), 305-326, 2007.
  5. Fonseca, M., Mexia, J.T., Zmyślony, R. Inference in normal models with commutative orthogonal block structure. Acta Comment. Univ. Tartu. Math., 12, 3-16, 2008.
  6. Fonseca, M., Mexia, J.T., Zmyślony, R. Least squares and generalized least squares in models with orthogonal block structure, J. Statist. Plann. Inference, 140(5), 1346-1352, 2010.
  7. Henderson, C. R. Statistical Methods in Animal Improvement: Historical Overview. In Gianola, Daniel and Hammond, Keith. Advances in Statistical Methods for Genetic Improvement of Livestock. Springer-Verlag Inc., 2-14, 1990.
  8. Houtman, A.M., Speed, T.P. Balance in designed experiments with orthogonal block structure. Ann. Statist., 11, 1069-1085, 1983.
  9. Jesus, V., Mexia, J.T., Zmyślony, R. Binary operations and canonical forms for factorial and related models, Linear Algebra Appl., 430(10) 2781-2797, 2009.
  10. Jordan, P., Neumann, J. von, Wigner, E. On an Algebraic Generalization of the Quantum Mechanical Formalism. Ann. of Math. (Princeton), 35(1), 29-64, 1934.
  11. Mexia, J.T. Best linear unbiased estimates, duality of F tests and the Scheffé multiple comparison method in the presence of controlled heteroscedasticity. Comput. Stat. Data An., 10(3) 271-281, 1990.
  12. Mexia, J.T., Vaquinhas, R., Fonseca, M., Zmyślony, R. COBS: Segregation, Matching, Crossing and Nesting. Latest Trends on Applied Mathematics, Simulation, Modeling, 4th International Conference on Applied Mathematics, Simulation, Modelling (ASM’10) 249-255, 2010.
  13. Nelder, J.A. The analysis of randomized experiments with orthogonal block st