A matrix approach to compare BLUEs under a linear regression model and its two competing restricted models with applications - Ren Xingwei (Demonstratio Mathematica)
Suppose that a weakly singular linear regression model M{\mathscr{M}} and its two competing restricted models M1{{\mathscr{M}}}_{1} and M2{{\mathscr{M}}}_{2} are given. We first compare the superiorities of the best linear unbiased estimators (BLUEs) under M{\mathscr{M}} and M1{{\mathscr{M}}}_{1} related to the covariance matrix criterion and derive some necessary and sufficient conditions. Based on these conditions and the covariance matrix criterion, we then compare the superiorities of the BLUEs under M1{{\mathscr{M}}}_{1} and M2{{\mathscr{M}}}_{2} and obtain some results. We finally apply these results to measure the influence of an observation on the BLUE.