Asymptotic theory for statistics based on cumulant vectors with applications
给出了任意多元分布的三阶和四阶累积量向量的渐近协方差显式公式，以及椭圆对称分布的累积量表达式，可用于推导新的偏度和峰度度量，并应用于独立成分分析和假设检验。
Abstract For any given multivariate distribution, explicit formulae for the asymptotic covariances of cumulant vectors of the third and the fourth order are provided here. General expressions for cumulants of elliptically symmetric multivariate distributions are also provided. Utilizing these formulae one can extend several results currently available in the literature, as well as obtain practically useful expressions in terms of population cumulants, and computational formulae in terms of commutator matrices. Results are provided for both symmetric and asymmetric distributions, when the required moments exist. New measures of skewness and kurtosis based on distinct elements are discussed, and other applications to independent component analysis and testing are considered.