Equations for the Edgeworth expansion of the distributions of the estimators in exploratory factor analysis and structural equation modeling are given. The equations cover the cases of non-normal data, as well as normal ones with and without known first-order asymptotic standard errors. When the standard errors are unknown, the distributions of the Studentized statistics are expanded. Methods of constructing confidence intervals of population parameters with arbitrary asymptotic confidence coefficients are given using the Cornish-Fisher expansion. Simulations are performed to see the usefulness of the asymptotic expansions in exploratory factor analysis with rotated solutions and confirmatory factor analysis. The results show that asymptotic expansion gives substantial improvement of approximation to the exact distribution constructed by simulations over the usual normal approximation.

中文翻译：

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非正态因素分析中估计量分布的渐近展开。

在探索性因子分析和结构方程建模中，给出了估计值分布的Edgeworth展开方程。这些方程式涵盖了非正态数据的情况，以及具有和不具有已知一阶渐近标准误差的正态数据的情况。当标准误差未知时，将扩展学生统计的分布。使用Cornish-Fisher展开给出了构造具有任意渐近置信系数的总体参数置信区间的方法。进行模拟以查看渐近展开在具有旋转解和验证性因子分析的探索性因子分析中的有用性。