Equivalence Analysis of Statistical Inference Results under True and Misspecified Multivariate Linear Models

This paper provides a complete matrix analysis on equivalence problems of estimation and inference results under a true multivariate linear model Y = X theta + Psi and its misspecified form Y = X theta + Z gamma + Psi with an augmentation part Z gamma through the cogent use of various algebraic formulas and facts in matrix analysis. The coverage of this study includes the matrix derivations of the best linear unbiased estimators under the true and misspecified models, and the establishment of necessary and sufficient conditions for the different estimators to be equivalent under the model assumptions.