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## Discussiones Mathematicae Probability and Statistics

2016 | 36 | 1-2 | 93-113
Tytuł artykułu

### Best unbiased estimates for parameters of three-level multivariate data with doubly exchangeable covariance structure and structured mean vector

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article author obtain the best unbiased estimators of doubly exchangeable covariance structure. For this purpose the coordinate free-coordinate approach is used. Considered covariance structure consist of three unstructured covariance matrices for three-level $m-$variate observations with equal mean vector over v points in time and u sites under the assumption of multivariate normality. To prove, that the estimators are best unbiased, complete statistics are used. Additionally, strong consistency is proven. Under the proposed model the variances of the estimators of covariance components are compared with the ones in the model in [11].
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
93-113
Opis fizyczny
Daty
wydano
2016
otrzymano
2016-09-15
Twórcy
autor
• Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516 Zielona Góra, Poland
Bibliografia
• [1] M. Fonseca, J.T. Mexia and R. Zmyślony, Least squares and generalized least squares in models with orthogonal block structure, J. Statistical Planning and Inference 140 (5) (2010), 1346-1352.
• [2] H. Drygas, The Coordinate-Free Approach to Gauss-Markov Estimation (Berlin, Heidelberg, Springer, 1970).
• [3] S. Gnot, W. Klonecki and R. Zmyślony, Uniformly minimum variance unbiased estimation in various classes of estimators, Statistics 8 (2) (1977), 199-210.
• [4] S. Gnot, W. Klonecki and R. Zmyślony, Best unbiased estimation: a coordinate free-approach, Probab. and Statis. 1 (1) (1980), 1-13.
• [5] P. Jordan, J. von Neumann and E. Wigner, On an algebraic generalization of the quantum mechanical formalism, Ann. Math. 35 (1) (1934), 29-64.
• [6] W. Kruskal, When are Gauss-Markov and Least Squares Estimators Identical, A Coordinate-Free Approach, Ann. Math. Stat. 39 (1) (1968), 70-75.
• [7] E.L. Lehmann and G. Casella, Theory of Point Estimation (Second Edition, Springer, 1998).
• [8] A. Roy and R. Leiva, Estimating and testing a structured covariance matrix for three-level multivariate data, Comm. Statist. Theory Methods 40 (11) (2011), 1945-1963.
• [9] A. Roy and M. Fonseca, Linear models with doubly exchangeable distributed errors, Comm. Statist. Theory Methods 41 (2012), 2545-2569.
• [10] A. Roy, R. Zmyślony, M. Fonseca and R. Leiva, Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure, J. Multivariate Analysis, 2016.
• [11] A. Roy, A. Kozioł, R. Zmyślony, M. Fonseca and R. Leiva, Best unbiased estimates for parameters of three-level multivariate data with doubly exchangeable covariance structure, Statistics 144 (2016), 81-90.
• [12] J.F. Seely, Quadratic subspaces and completeness, Ann. Math. Statist. 42 (2) (1971), 710-721.
• [13] J.F. Seely, Completeness for a family of multivariate normal distributions, Ann. Math. Statist. 43 (1972), 1644-1647.
• [14] J.F. Seely, Minimal sufficient statistics and completeness for multivariate normal families, Sankhya (Statistics). Indian J. Statist. Ser. A 39 (2) (1977), 170-185.
• [15] R. Zmyślony, On estimation of parameters in linear models, Appl. Math. XV (1976), 271-276.
• [16] R. Zmyślony, A characterization of best linear unbiased estimators in the general linear model, Lecture Notes in Statistics 2 (1978), 365-373.
• [17] R. Zmyślony, Completeness for a family of normal distributions, Math. Stat. Banach Center Publications 6 (1980), 355-357.
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Bibliografia
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