Standard errors of the principal component loadings for unstandardized and standardized variables

The asymptotic standard errors of the estimates of the principal component loadings for standardized variables are derived under the assumption of multivariate normality. The standard errors are obtained for the usual unrotated case where a loading matrix is orthogonal and for the cases with orthogonally or obliquely rotated components. The corresponding standard errors for unstandardized variables and the asymptotic correlations among the estimators of the parameters for the unstandardized and standardized variables are simultaneously derived, together with the standard errors for the standardized variables. Results of a simulation illustrate the accuracy of the theoretical asymptotic standard errors and correlations.