General canonical correlations with applications to group symmetry models

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Andersson, Steen A.²  Crawford, Jesse B.¹ 

[1] Tarleton State Univ, Dept Math, Stephenville, TX 76402 USA

[2] Indiana Univ, Dept Stat, Bloomington, IN 47405 USA

关键词: Canonical correlation;    Canonical covariate;    Eigenvalue;    Eigenvector;    Group symmetry model;    Maximal invariant;   

DOI  :  10.1016/j.jmva.2010.03.010

来源: Elsevier

【 摘 要 】

In this paper, we define general canonical correlations, which generalize the canonical correlations developed by Hotelling, and general canonical covariate pairs, the corresponding linear statistic. We also define canonical variance distances with corresponding canonical distance variates. In a rather broad setting, these parameters and their corresponding linear statistics are characterized in terms of certain eigenvalues and eigenvectors. For seven of the ten group symmetry testing problems discussed in Andersson, Brons, and Jensen (1983) [4], these are the eigenvalues used to represent the maximal invariant statistic, and additional observations regarding the canonical correlations are made for these testing problems. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free