A new analysis of the relationships between a general linear model and its mis-specified forms

Assume that a real linear regression model is presented in certain mis-specified form. Under this situation, the predictions and estimations of all unknown parameters in the mis-specified model will lead to wrong conclusions in the statistical inference of the real model. The purpose of this paper is to characterize the relationships between the best linear unbiased predictors (BLUPs) of all unknown parameters under a real linear model and its mis-specified forms via some exact algebraic tools in matrix theory.