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Linear sufficiency and completeness in an incorrectly specified general Gauss-Markov model. (English) Zbl 0611.62073
Let $$M=\{Y,X\beta,V\}$$ and $$M_ 0=\{Y,X_ 0\beta_ 0,V_ 0\}$$ be two general Gauss-Markov models and J, $$J_ 0$$ two sets of linear statistics having certain properties with respect to the models M, $$M_ 0$$. The paper deals with the problem to give necessary and sufficient conditions on M and $$M_ 0$$ such that $$J_ 0\subset J$$ with special attention to classes J, $$J_ 0$$ of linearly sufficient, minimal sufficient and complete statistics, respectively. Since these concepts can be defined purely in concepts of linear algebra, such characterizations are also possible with the help of these concepts. A comparison is also made with similar conditions for the sets of BLUEs in both models.
Reviewer: O.Krafft

##### MSC:
 62J05 Linear regression; mixed models 62B05 Sufficient statistics and fields 15A24 Matrix equations and identities