Abstract
Necessary and sufficient conditions are derived for the inclusions \(J_0 \subset J\) and \(J_0^* \subset J^* \) to be fulfilled where \(J_0 ,J_0^* {\text{ and }}J,J^* \) are some classes of invariant linearly sufficient statistics (Oktaba, Kornacki, Wawrzosek (1988)) corresponding to the Gauss-Markov models \(GM_0 = (y,X_0 \beta _0 ,\sigma _0^2 V_0 ){\text{ and }}GM = (y,X\beta ,\sigma ^2 V)\), respectively.
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Kornacki, A. Stability of invariant linearly sufficient statistics in the general Gauss-Markov model. Applications of Mathematics 42, 71–77 (1997). https://doi.org/10.1023/A:1022244727376
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DOI: https://doi.org/10.1023/A:1022244727376