Several Cases Of The Admissibility Of Error Variance In Linear Models

This paper studies several cases including the class of homogeneous estimates, the non-homogeneous estimators, the unconstrained model and constrained models the error variance in linear model problem .Some theoretical results are obtained. The whole paper is divided into five parts .The first section, an overview is given part of the thesis and related background knowledge. In the second section, gives a general need to use the paper to allow the study of need to use the basic knowledge, the second type of knowledge and concepts relating to admissibility. In the third section, under the assumption that the linear model H , summarizes previous estimates in homogeneous categories: D + {Y 'AY : A+ 0} in the results, geting Theorem (3.2.1) Theorem (3.2.2). In the fourth section, still under the assumption of the linear model H , after a series of Proof and derivation, have been estimated in the non-homogeneous class: D2 + {( BY + a ) ( BY + a ): a + Rm}When the design matrix is full rank matrix that is: rank ( X )+ n and the matrix that is: X + I, more special case of two kinds of linear models to allow the necessary and sufficient condition that the theorem (4.2.1), Theorem (4.2.2).In the fifth chapter, Chapter III of this chapter is based on the linear model of innovation by adding a constraint: 2, the linear model H 1, and then obtained under the assumption that: H 1 the constraint model error variance to allow the necessary and sufficient condition that Theorem (5.2.1). Idea of writing this paper is: first discuss the model and then discuss the non-binding constraint model, and then estimated from the class of homogeneous estimates of non-homogeneous class, the content is a summary of previous results and their own innovation, promotion of the previous studies results, non-rich to allow variance in theory, in particular, parameters are bound under the circumstances.