Asymptotic Distributions in Canonical Correlation Analysis and Other Multivariate Procedures for Nonnormal Populations
研究了总体四阶矩有限时典型相关分析的渐近理论，发现样本典型相关系数和检验统计量的渐近分布依赖于总体四阶累积量，对非正态性敏感；但在椭圆总体下形式简单，可用修正卡方检验零系数假设。
An asymptotic theory for canonical correlation analysis is given for multivariate populations with finite fourth moments. The asymptotic distributions of the sample canonical correlation coefficients and of statistics used for testing hypotheses about the population coefficients involve the fourth 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. Finally we note that, when sampling from elliptical populations, the asymptotic distributions of test statistics used in some other multivariate procedures are similarly simple.