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

Bo Jiang () and Yongge Tian
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Bo Jiang: College of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China
Yongge Tian: College of Business and Economics, Shanghai Business School, Shanghai 201400, China

Mathematics, 2022, vol. 11, issue 1, 1-16

Abstract: This paper provides a complete matrix analysis on equivalence problems of estimation and inference results under a true multivariate linear model Y = X Θ + Ψ and its misspecified form Y = X Θ + Z Γ + Ψ with an augmentation part Z Γ 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.

Keywords: augmentation; BLUE; BLUP; Kronecker product; multivariate linear model; parameter matrix; rank; reduced model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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