Resumen
Se discute el problema de existencia del mejor estimador lineal insesgado (BLUE) para el valor esperado de una distribución en un contexto libre de coordenadas, usando un modelo de curvas de crecimiento multivariado. También se presenta la igualdad del estimador anterior con el estimador de mínimos cuadrados ordinarios (OLSE). Se prueba que las diferentes formas de expresar las condiciones necesarias y suficientes para demostrar las propiedades anteriores son independientes de la matriz de diseño del modelo entre individuos.
Palabras clave
Citas
Aitken, A. C. (L934). "On least squares and linear combination of observations," Proc. Roy. Soc. Edinburgh, Sec. A, 55, 42-47.
Arnold, S. F. (1979). "A coordinate-free approach to finding optimal procedures for repeated measures designs," Ann. Statist., 7, 812-822.
Baksalary, J. K., & Kala, R. (1976). "Criteria for estimability in multivariate linear models," Math. Operationsforsch. Statist. Ser. Statist., 7, 5-9.
Baksalary, J. K., & van Eijnsborgen, A. C. (1988). "A comparison of two criteria for ordinary least squares estimators to be best linear unbiased estimators," Amer. Statist., 42, 205-208.
Beganu, G. (1987a). "Estimation of regression parameters in a covariance linear model," Stud. Cerc. Mat., 39, 3-10.
Beganu, G. (1987b). "Estimation of covariance components in linear models. A coordinate-free approach," Stud. Cerc. Mat., 39, 228-233.
Beganu, G. (2003). "The existence conditions of the best linear unbiased estimators of the fixed effects," Econom. Comput. Econom. Cybernet. Studies and Research, 36, 95-102.
Beganu, G. (2005). "On Gram-Schmidt orthogonalizing process of design matrices in linear models as estimating procedures of covariance components," Rev. R. Acad. Cien., Serie A Mat., 99(2), 187-194.
Beganu, G. "Quadratic estimators of covariance components in a multivariate mixed linear model," Statist. Methods and Applications (to appear in 2007).
Beganu, G. "On the equality of the ordinary least squares estimators and the best linear unbiased estimators in multivariate growth-curve models," Rev. R. Acad. Cien., Serie A Mat. (to appear in 2007).
Orygas, H. (1972). "A note on Gauss-Markov estimation in multivariate linear models," Colloquia Mathematica Societatis Janos Bolyai, 9. European Meeting of Statisticians Budapest, 181-190.
Orygas, H. (1975). "Estimation and prediction for linear models in general spaces," Math. Operationsforsch. Statist., ser. Statist., 8, 301-324.
Eaton, M. L. (1970). "Gauss-Markov estimation for multivariate linear models: A coordinate-free approach," Ann. Math. Statist., 2, 528-538.
Haberman, S. I. (1975). "How much do Gauss-Markov and least squares estimates differ? A coordinate-free approach," Ann. Statist., 3, 982-990.
Harville, O. A. (1976). "Extension of the Gauss-Markov theorem to include the estimation of random effects," Ann. Statist., 4, 334-395.
Klotz, J. (1978). "Simultaneous estimation of expectation and covariance matrices in linear models," Math. Operationsforsch. Statist., 9, 443-478.
Kruskal, W. (1968). "When are Gauss-Markov and least squares estimators identical? A coordinate-free approach," Ann. Math. Statist., 39, 70-75.
Lange, N., & Laird, N. M. (1989). "The effect of covariance structure on variance estimation in balanced growth-curve models with random parameters," J. Amer. Statist. Assoc., 84, 241-247.
Milliken, G. A. (1971). "New criteria for estimability for linear models," Ann. Math. Statist., 42, 1588-1594.
Puntanen, S., & Styan, G. P. H. (1989). "The equality of the ordinary least squares estimator and the best linear unbiased estimator," Amer. Statist., 43, 153-161.
Puntanen, S., Styan, G. P. H., & Tian, Y. (2005). "Three rank formulas associated with the covariance matrices of the BLUPs and the OLSE in the general linear model," Econometric Theory, 21, 659-664.
Qian, H., & Tian, Y. (2006). "Portion superfluous observations," Econometric Theory, 22, 525-536.
Rao, C. R. (1967). "Least squares theory using an estimated dispersion matrix and its application to measurement of signals," Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 1) eds. L. M. Le Cam and J. Neyman, Berkeley: University of California Press, 355-372.
Rao, C. R. (1973). Linear Statistical Inference and Its Applications (2nd ed.), John Wiley, New York.
Reinsel, C. G. (1982). "Multivariate repeated-measurement or growth curve models with multivariate random effects covariance structure," J. Amer. Statist. Assoc., 77, 190-195.
Reinsel, C. G. (1934). "Estimation and prediction in a multivariate random effects generalized linear models," J. Amer. Statist. Assoc., 79, 406-414.
Seely, J. (1970a). "Linear space and unbiased estimation," Ann. Math. Statist., 41, 1725-1734.
Seely, J. (1970b). "Linear space and unbiased estimation: Application to the mixed linear models," Ann. Math. Statist., 41, 1735-1748.
Zyskind, G. (1967). "On canonical forms, non-negative covariance matrices, and best and simple least squares linear estimators in linear models," Ann. Math. Statist., 38, 1092-1109.
Zyskind, G., & Martin, F. B. (1969). "On best linear estimation and a general Gauss-Markoff theorem in linear models with arbitrary non-negative structures," SIAM J. Appl. Math., 17, 1190-1202.
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