ASYMPTOTIC DISTRIBUTIONS IN CANONICAL CORRELATION-ANALYSIS AND OTHER MULTIVARIATE PROCEDURES FOR NON-NORMAL POPULATIONS
成果类型：
Article
署名作者：
MUIRHEAD, RJ; WATERNAUX, CM
署名单位：
Harvard University
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
发表日期：
1980
页码：
3143
关键词：
摘要：
An asymptotic theory for canonical correlation analysis is given for multivariate populations with finite-4th moments. Asymptomatic distributions of the sample canonical correlation coefficients and of statistics used for testing hypotheses about the population coefficients involve the 4th order cumulants of the parent population and are sensitive to departures from normality. These asymptotic distributions have surprisingly simple forms in the case of elliptical populations; here a modified test statistic with a chi-squared approximation can be used for testing the hypothesis that some of the population coefficients are zero. When sampling from elliptical populations, asymptotic distributions of test statistics used in some other multivariate procedures are similarly simple.