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Stability of invariant linearly sufficient statistics in the general Gauss-Markov model

Authors:	Andrzej Kornacki

Institution:	(1) Institute of Applied Mathematics, University of Agriculture, Akademicka 13, 20–934 Lublin, Poland

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.

Keywords:	Gauss-Markov model linearly sufficient statistics invariant linearly sufficient statistics
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