Linear Model Parameter Estimation Admissibility

In real life and science research, we can meet with a lot of data which are coincided with linear model. This paper defines strictly general Gauss-Markovmodel discussed in many papers (also written G-M model)Considing estimates of G-M model (or linear functional Sβ of β ), admissibility is firstly required in these estimates. So this paper discusses the admissibility of linear estimators in general linear model and general linear model varied in a incomplete ellipsoia of the G-M model.In the linear modelloss function, based on the results un the paper [13], this paper puts forward the sufficient and necessary conditions of LY in the class of homogenous linear estimators and LY + c in the class of nonhomgenous linear estimators for a linear estimator of Sβ to be admissible, which generalizes some findings in paper [12]. The general admissibility in the multivariate regression model is extended in the following. In the linear model varied in a incomplete ellipsoidal restriction and under quadratic loss function, the admissibility has an unique and interesting phenomenon, which is that the admissibility of linear estimator among the class of all linear estimators is independent on ellipsoidal center, in a word, the admissibility of linear estimator among the class of all linear estimator has robustness, while, the admissibility of homogeneous linear estimator among...