zbMATH — the first resource for mathematics

Some remarks on general linear model with new regressors. (English) Zbl 1312.62091
Summary: Assume that an original general linear model is misspecified by adding some new regressors. We investigate in such a case relationships between the best linear unbiased estimators under the two models. In particular, we give necessary and sufficient conditions for the best linear unbiased estimators to be equal under the two models.

62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
Full Text: DOI
[1] Alalouf, I. S.; Styan, G. P.H., Characterizations of estimability in the general linear model, Ann. Statist., 7, 194-200, (1979) · Zbl 0398.62053
[2] Bhimasankaram, P.; Jammalamadaka, S. R., Updates of statistics in a general linear model: a statistical interpretation and applications, Comm. Statist. Simulation Comput., 23, 789-801, (1994) · Zbl 0825.62062
[3] Drygas, H., The coordinate-free approach to Gauss-Markov estimation, (1970), Springer Heidelberg · Zbl 0215.26504
[4] Jammalamadaka, S. R.; Sengupta, D., Changes in the general linear model: a unified approach, Linear Algebra Appl., 289, 225-242, (1999) · Zbl 0933.62060
[5] Jammalamadaka, S. R.; Sengupta, D., Inclusion and exclusion of data or parameters in the general linear model, Statist. Probab. Lett., 77, 1235-1247, (2007) · Zbl 1115.62066
[6] Marsaglia, G.; Styan, G. P.H., Equalities and inequalities for ranks of matrices, Linear Multilinear Algebra, 2, 269-292, (1974) · Zbl 0297.15003
[7] Rao, C. R., Unified theory of linear estimation, Sankhyā Ser. A, 33, 371-394, (1971) · Zbl 0236.62048
[8] Rao, C. R., Representations of best linear unbiased estimators in the Gauss-markoff model with a singular dispersion matrix, J. Multivariate Anal., 3, 276-292, (1973) · Zbl 0276.62068
[9] Rao, C. R., Estimations of paramters in a linear model, Ann. Statist., 4, 1023-1037, (1976) · Zbl 0336.62055
[10] Rao, C. R., A lemma on optimization of matrix function and a review of the unified theory of linear estimation, (Dodge, Y., Statistical Data Analysis and Inference, (1989), North Holland), 397-417 · Zbl 0735.62066
[11] Searle, S. R., The matrix handling of BLUE and BLUP in the mixed linear model, Linear Algebra Appl., 264, 291-311, (1997) · Zbl 0889.62059
[12] Tian, Y., Some decompositions of OLSEs and BLUEs under a partitioned linear model, Internat. Statist. Rev., 75, 224-248, (2007)
[13] Tian, Y., On an additive decomposition of the BLUE in a multiple partitioned linear model, J. Multivariate Anal., 100, 767-776, (2009) · Zbl 1155.62045
[14] Tian, Y., On equalities of estimations of parametric functions under a general linear model and its restricted models, Metrika, 72, 313-330, (2010) · Zbl 1197.62020
[15] Tian, Y., Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method, Nonlinear Anal., 75, 717-734, (2012) · Zbl 1236.65070
[16] Tian, Y., On properties of BLUEs under general linear regression models, J. Statist. Plann. Inference, 143, 771-782, (2013) · Zbl 1428.62344
[17] Tian, Y.; Takane, Y., Some properties of projectors associated with the WLSE under a general linear model, J. Multivariate Anal., 99, 1070-1082, (2008) · Zbl 1141.62043
[18] Tian, Y.; Zhang, J., Some equalities for estimations of partial coefficients under a general linear regression model, Statist. Papers, 52, 911-920, (2011) · Zbl 1229.62075
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.