GENERAL DEFINITION AND DECOMPOSITION OF PROJECTORS AND SOME APPLICATIONS TO STATISTICAL PROBLEMS

被引：50

作者：

RAO, CR ^{[1
]}

YANAI, H ^{[1
]}

机构：

[1] CHIBA UNIV,CHIBA 280,JAPAN

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 1979年 / 3卷 / 01期

关键词：

Canonical Correlations; Constrained g-inverse; Gauss-Markoff Model; Generalized Inverse; Multiple Correlation; Orthogonal Projector;

D O I：

10.1016/0378-3758(79)90038-7

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A general definition of a set of projectors for decomposing a vector as the sum of vectors belonging to disjoint subspaces not necessarily spanning the whole space is given. Such projectors are defined only over the union of the disjoint subspaces. But their extension to the whole space is of some interest in statistical problems. Explicit expressions are obtained for projectors and their extensions in terms of matrices spanning the subspaces and g-inverses. Decomposition of a projector as the sum of projectors on subspaces is obtained and applied to problems arising in correlation analysis, analysis of variance and estimation of parameters in the Gauss-Markoff model. © 1979.

引用

页码：1 / 17

页数：17

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