Linear and Quadratic Sufficiency and Commutativity

被引：1

作者：

Ferreira, Sandra S. ^{[1
]}

Ferreira, Dario ^{[2
]}

Nunes, Celia ^{[2
]}

机构：

[1] Univ Beira Interior, Dept Math, P-6200 Covilha, Portugal

[2] Univ Beira Interior, Ctr Math, P-6200 Covilha, Portugal

来源：

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2012), VOLS A AND B | 2012年 / 1479卷

关键词：

Linear sufficiency; quadratic sufficiency; orthogonal projection; linear completeness;

D O I：

10.1063/1.4756496

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a mixed model let T be the orthogonal projection matrix on the range space spanned by the mean vector. If the model has variance-covariance matrix sigma V-2 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 Moore-Penrose inverse of V is quadratic sufficient whenever T and V commute.

引用

页码：1694 / 1697

页数：4

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