# Article

 Title: Stability of invariant linearly sufficient statistics in the general Gauss-Markov model (English) Author: Kornacki, Andrzej Language: English Journal: Applications of Mathematics ISSN: 0862-7940 Volume: 42 Issue: 1 Year: 1997 Pages: 71-77 Summary lang: English . Category: math . Summary: Necessary and sufficient conditions are derived for the inclusions $J_0\subset J$ and $J_0^{*}\subset J^{*}$ to be fulfilled where $J_0$, $J_0^{*}$ and $J$, $J^{*}$ are some classes of invariant linearly sufficient statistics (Oktaba, Kornacki, Wawrzosek (1988)) corresponding to the Gauss-Markov models $GM_0=(y,X_0\beta _0,\sigma _0^2V_0)$ and $GM=(y,X\beta ,\sigma ^2V)$, respectively. (English) Keyword: Gauss-Markov model Keyword: linearly sufficient statistics Keyword: invariant linearly sufficient statistics MSC: 62A01 MSC: 62B05 MSC: 62F10 MSC: 62J05 idZBL: Zbl 0898.62003 idMR: MR1426681 DOI: 10.1023/A:1022244727376 . Date available: 2009-09-22T17:53:37Z Last updated: 2015-05-20 Stable URL: http://hdl.handle.net/10338.dmlcz/134345 . Reference: [1] J.K. Baksalary, T. Mathew: Linear sufficiency and completeness in an incorrectly specified general Gauss-Markov model.Sankhyā, Ser A. 48 (1986), 169–180. MR 0905457 Reference: [2] H. Drygas: Sufficiency and completeness in the general Gauss-Markoff model.Sankhyā, Ser A. 45 (1983), 88–98. MR 0749356 Reference: [3] R. Kala: Projectors and linear estimation in general linear models.Comm. Statistics—A, Theory Methods 10 (1981), 849–873. Zbl 0465.62060, MR 0625196, 10.1080/03610928108828078 Reference: [4] T. Mathew, P. Bhimasankaram: Optimality of BLUE$^{\prime }s$ in a general linear model with an incorrect design matrix.J. Statist Plann. Inference 8 (1983), 315–329. MR 0729248, 10.1016/0378-3758(83)90048-4 Reference: [5] W. Oktaba, A. Kornacki, J. Wawrzosek: Invariant linearly sufficient transformations of the general Gauss-Markoff model.Scand. J Statist. 15 (1988), 117–124. MR 0968158 Reference: [6] C.R. Rao: Unified theory of linear estimation.Sankhyā A 35 (1971), 371–394. Zbl 0236.62048, MR 0319321 Reference: [7] C.R. Rao, S.K. Mitra: Generalized Inverse of Matrices and its Applications.Wiley, New York, 1971. MR 0338013 .

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