# Article

Full entry | PDF   (0.2 MB)
Keywords:
Gauss-Markov model; linearly sufficient statistics; invariant linearly sufficient statistics
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.
References:
[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
[2] H. Drygas: Sufficiency and completeness in the general Gauss-Markoff model. Sankhyā, Ser A. 45 (1983), 88–98. MR 0749356
[3] R. Kala: Projectors and linear estimation in general linear models. Comm. Statistics—A, Theory Methods 10 (1981), 849–873. MR 0625196 | Zbl 0465.62060
[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
[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
[6] C.R. Rao: Unified theory of linear estimation. Sankhyā A 35 (1971), 371–394. MR 0319321 | Zbl 0236.62048
[7] C.R. Rao, S.K. Mitra: Generalized Inverse of Matrices and its Applications. Wiley, New York, 1971. MR 0338013

Partner of