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非正态总体下典型相关分析及其他多元方法的渐近分布AI 解读

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…

非正态总体下典型相关分析及其他多元方法的渐近分布AI 解读

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…

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非正态总体下样本协方差矩阵特征根的渐近分布AI 解读

The distribution of the characteristic roots of the sample covariance matrix is studied for multivariate populations with finite fourth cumulants. For large sample sizes, the asymptotic forms of the marginal and joint distributions are given. For moderate and small sample sizes, empirical sampling techniques are used: various trivariate models are simulated, and the distributions of the sample roots are empirically observed. It is shown that the distributional results for a…