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

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  • Bo Jiang

    (College of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China
    These authors contributed equally to this work.)

  • Yongge Tian

    (College of Business and Economics, Shanghai Business School, Shanghai 201400, China
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Bo Jiang & Yongge Tian, 2022. "Equivalence Analysis of Statistical Inference Results under True and Misspecified Multivariate Linear Models," Mathematics, MDPI, vol. 11(1), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:182-:d:1019173
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    References listed on IDEAS

    as
    1. Nel, Daan G., 1997. "Tests for Equality of Parameter Matrices in Two Multivariate Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 29-37, April.
    2. Shengjun Gan & Yuqin Sun & Yongge Tian, 2017. "Equivalence of predictors under real and over-parameterized linear models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(11), pages 5368-5383, June.
    3. Yongge Tian, 2015. "A new derivation of BLUPs under random-effects model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 905-918, November.
    4. Jammalamadaka, S. Rao & Sengupta, D., 2007. "Inclusion and exclusion of data or parameters in the general linear model," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1235-1247, July.
    5. Jan R. Magnus & J. Durbin, 1999. "Estimation of Regression Coefficients of Interest When Other Regression Coefficients Are of No Interest," Econometrica, Econometric Society, vol. 67(3), pages 639-644, May.
    6. Jun, Sung Jae & Pinkse, Joris, 2009. "Adding Regressors To Obtain Efficiency," Econometric Theory, Cambridge University Press, vol. 25(1), pages 298-301, February.
    7. Lu, Changli & Gan, Shengjun & Tian, Yongge, 2015. "Some remarks on general linear model with new regressors," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 16-24.
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