Linear and quadratic sufficiency and commutativity
Abstract
Given a mixed model let T be the orthogonal projection matrix on the range space spanned by the mean vector. If the model has variancecovariance matrix σ^{2}V we use commutative Jordan algebras to show that Ty is both linear sufficient and linear complete and that Ty, y'V^{+}y with V^{+} the MoorePenrose inverse of V is quadratic sufficient whenever T and V commute.
 Publication:

Numerical Analysis and Applied Mathematics ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics
 Pub Date:
 September 2012
 DOI:
 10.1063/1.4756496
 Bibcode:
 2012AIPC.1479.1694F
 Keywords:

 covariance matrices;
 02.10.Yn;
 02.60.Dc;
 Matrix theory;
 Numerical linear algebra