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A new analysis of the relationships between a general linear model and its mis-specified forms
Yongge Tian,Bo Jiang 한국통계학회 2017 Journal of the Korean Statistical Society Vol.46 No.2
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.
How to Characterize Equalities for the Moore-Penrose Inverse of a Matrix
Yongge Tian KYUNGPOOK UNIVERSITY 2001 Kyungpook mathematical journal Vol.41 No.1
We present in this paper some formulas for ranks of matrices and then use them to characterize various equalities related to the Moore-Penrose inverse of a matrix.
On equivalence of predictors/estimators under a multivariate general linear model with augmentation
Bo Jiang,Yongge Tian 한국통계학회 2017 Journal of the Korean Statistical Society Vol.46 No.4
Assume that a true multivariate general linear model for an observed random matrix is over-parameterized by adding some new regressors due to model uncertainty. Then predictors and estimators of parameter spaces in the true and over-parameterized models are not necessarily the same. In this article, we study the comparison problem of predictors/ estimators of parameter spaces under the two models. In particular, we derive necessary and sufficient conditions for the best linear unbiased predictors/best linear unbiased estimators of the parameter spaces to be equivalent under the two models.