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2003 | 23 | 2 | 175-201
Tytuł artykułu

Estimators and tests for variance components in cross nested orthogonal designs

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Języki publikacji
EN
Abstrakty
EN
Explicit expressions of UMVUE for variance components are obtained for a class of models that include balanced cross nested random models. These estimators are used to derive tests for the nullity of variance components. Besides the usual F tests, generalized F tests will be introduced. The separation between both types of tests will be based on a general theorem that holds even for mixed models. It is shown how to estimate the p-value of generalized F tests.
Twórcy
  • Department of Mathematics, Faculty of Science and Technology, New University of Lisbon, Monte da Caparica 2829-516 Caparica, Portugal
  • Department of Mathematics, Faculty of Science and Technology, New University of Lisbon, Monte da Caparica 2829-516 Caparica, Portugal
  • Institute of Mathematics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland
Bibliografia
  • [1] M. Fonseca, J.T. Mexia and R. Zmyślony, Estimating and testing of variance components: an application to a grapevine experiment, Biometrical Letters 40 (1) (2003), 1-7.
  • [2] M. Fonseca, J.T. Mexia and R. Zmyślony, Exact distribution for the generalized F tests, Discuss. Math.-Probability and Satatistics 1,2 (2002), 37-51.
  • [3] A.I. Khuri, Direct Products: A powerful tool for the analysis of balanced data, Commun. Stat. Theory, 11 (1977), 2903-2929.
  • [4] A.I. Khuri, T. Matthew and B.K. Sinha, Statistical Tests for Mixed Linear Models, Wiley 1997.
  • [5] M. Loeve, Probability Theory, D. van Nostrand Company 1963.
  • [6] J. Seely and G. Zyskind, Linear spaces and minimum variance unbiased estimation, Ann. Math. Stat. 42 (1971), 691-703.
  • [7] J. Seely and G. Zyskind, Quadratic subspaces and completeness, Ann. Math. Stat. 42 (1971), 710-721.
  • [8] J. Seely, Minimal sufficient statistics and completeness for multivariate normal families, Sankhya, Ser. (A) 39 (1977), 170-185.
  • [9] T.A. Severini, Likelihood Methods in Statistics, Oxford University Press 2000.
  • [10] W.H. Steeb, Kronecker Product and Applications, Manheim 1991.
  • [11] R. Zmyślony, Completeness for a family of normal distributions, Mathematical Statistics, Banach Cent. Publ. 6 (1980), 355-357.
  • [12] A. Michalski and R. Zmyślony, Testing hypotheses for variance components in mixed linear models, Statistics (3-4) 27 (1996), 297-310.
  • [13] R. Zmyślony and S. Zontek, On robust estimation of variance components via von Mises functionals, Discuss. Math.-Algebra and Stoch. Methods, 15 (2) (1995), 349-362.
  • [14] A. Michalski and R. Zmyślony, Testing hypotheses for linear functions of parameters in mixed linear models, Tatra Mt. Math. Publ. 17 (1999), 103-110.
  • [15] S. Zontek, Robust estimation in linear models to spatially located sensors and random input, Tatra Mountain Publications 17 (1999), 301-310.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1043
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