It is well known that there were proved several necessary and sufficient conditions for the ordinary least squares estimators (OLSE) to be the best linear unbiased estimators (BLUE) of the fixed effects in general linear models. The purpose of this article is to verify one of these conditions given by Zyskind [39, 40]: there exists a matrix Q such that ΩX = XQ, where X and Ω are the design matrix and the covariance matrix, respectively. It will be shown the accessibility of this condition in some multivariate growth-curve models, establishing the known result regarding the equality between OLSE and BLUE in this type of linear models.
Es bien sabido que existen demostraciones de varias condiciones necesarias y suficientes para que los estimadores ordinarios de mínimos cuadrados (OLSE) sean los estimadores lineales insesgados óptimos (BLUE) de modelos lineales generales con efectos fijos. El propósito de este artículo es comprobar una de esas condiciones dada por Zyskind [39, 40]: existe una matrix Q tal que ΩX = XQ, donde X y Ω son la matriz de diseño y la matriz de covarianza, respectivamente. Se demostrará la accesibilidad de esta condición en algunos modelos multivariantes de curvas de crecimiento, estableciendo el resultado conocido teniendo en cuenta la igualdad entre OLSE y BLUE en este tipo de modelos lineales.
@article{urn:eudml:doc:41664,
title = {On the equality of the ordinary least squares estimators and the best linear unbiased estimators in multivariate growth-curve models.},
journal = {RACSAM},
volume = {101},
year = {2007},
pages = {63-70},
zbl = {1137.62034},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41664}
}
Beganu, Gabriela. On the equality of the ordinary least squares estimators and the best linear unbiased estimators in multivariate growth-curve models.. RACSAM, Tome 101 (2007) pp. 63-70. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41664/