Applications of asymptotic theory to factor analysis and structural equation modeling

(1)因子分析(FA)中渐近偏差的推导在因子分析中，因子负荷的估计量是最重要的。(2)主成分分析(PCA)中渐近偏差的导出主成分分析(PCA)中主成分分析(PCA)的渐近偏差在非正态下得到了正、斜旋转分量载荷估计量的渐近偏差。(3)参数估计量的渐近展开协方差结构中参数估计的Edgeworth展开式。(4)利用结构方程模型中隐函数中的一个推广公式，给出了参数估计量的高阶渐近标准误差。(5)结构方程模型中参数估计的渐近偏差的渐近稳健性的推导。在某些条件下，得到了结构模型中参数估计量的正态理论渐近偏差的渐近稳健性。

(1)Derivation of the asymptotic bias in factor analysis (FA)In factor analysis, the estimators of factor loadings are of primary interest. So, the asymptotic biases of the estimators of factor loadings are derived under nonnormality, where the loadings are possibly orthogonally rotated.(2)Derivation of the asymptotic bias in principal component analysis (PCA)In principal component analysis, the asymptotic biases of the orthogonally or obliquely rotated component loading estimators are derived under nonnormality.(3)Asymptotic expansion of the parameter estimatorsEdgeworth expansions of the parameter estimators in covariance structures are given under nonnormality. To have the confidence intervals of the parameters, the Cornish-Fisher expansions of the Studentized estimators are derived.(4)Higher-order asymptotic standard errorHigher-order asymptotic standard errors of the parameter estimators are provided using an extended formula in implicit functions in structural equation modeling.(5)Derivation of the asymptotic robustness of the asymptotic biases in structural equation modelingThe asymptotic robustness of the normal-theory asymptotic biases of the parameter estimators in structural models are derived under some conditions against the violation of the assumption of normality.