The Shape of Correlation Matrices
作者:
PeterJ. Rousseeuw,
Geert Molenberghs,
期刊:
The American Statistician
(Taylor Available online 1994)
卷期:
Volume 48,
issue 4
页码: 276-279
ISSN:0003-1305
年代: 1994
DOI:10.1080/00031305.1994.10476079
出版商: Taylor & Francis Group
关键词: Convexity;Correlation coefficient;Elliptical tetrahedron;Graphical display;Range restrictions
数据来源: Taylor
摘要:
A correlation matrix between three variables has to satisfy certain conditions. Such a matrix essentially contains three numbers and thus can be represented by a point in three dimensions. The set of all possible correlation matrices yields a convex solid body with an uncommon shape. All its cross sections perpendicular to the axes are ellipses. At the same time, its surface contains the vertices and edges of a regular tetrahedron. Another unusual shape is obtained for banded correlation matrices between four variables.
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