Covariance Structure Analysis with Heterogeneous Kurtosis Parameters
研究了一类边际分布具有异质峰度参数的多元分布中的协方差结构分析，提出利用峰度估计调整权重矩阵以得到渐近有效的结构参数估计，并用两个实际数据集演示。
This paper discusses the analysis of covariance structures in a wide class of multivariate distributions whose marginal distributions may have heterogeneous kurtosis parameters. Elliptical distributions often used as a generalization of the normal theory are members of this class. It is shown that a simple adjustment of the weight matrix of normal theory, using kurtosis estimates, results in an asymptotically efficient estimator of structural parameters within the class of estimators that minimize a general discrepancy function. Results are obtained for arbitrary covariance structures as well as those that meet a scale invariance assumption. Two real data sets are analyzed for illustrative purposes.